18 September 2013 02:50:46 PM
PROB_PRB
C++ version.
Test the PROB library.
TEST001
For the ANGLE PDF:
ANGLE_CDF evaluates the CDF;
Parameter N = 5
PDF argument X = 0.5
CDF value = 0.0107809
TEST002
For the ANGLE PDF:
ANGLE_PDF evaluates the PDF;
Parameter N = 5
PDF argument X = 0.5
PDF value = 0.0826466
TEST003
For the ANGLE PDF:
ANGLIT_MEAN computes the mean;
Parameter N = 5
PDF mean = 1.5708
TEST004
For the Anglit PDF:
ANGLIT_CDF evaluates the CDF;
ANGLIT_CDF_INV inverts the CDF.
ANGLIT_PDF evaluates the PDF;
X PDF CDF CDF_INV
-0.299105 0.186098 0.218418 -0.299105
0.574842 0.934378 0.956318 0.574842
0.359757 0.99783 0.829509 0.359757
0.0618531 0.788954 0.561695 0.0618531
-0.0851032 0.577115 0.415307 -0.0851032
-0.525341 -0.262184 0.0661187 -0.525341
-0.253093 0.275599 0.257578 -0.253093
-0.447402 -0.109188 0.109957 -0.447402
-0.574484 -0.355613 0.043829 -0.574484
0.135623 0.87071 0.633966 0.135623
TEST005
For the Anglit PDF:
ANGLIT_MEAN computes the mean;
ANGLIT_SAMPLE samples;
ANGLIT_VARIANCE computes the variance.
PDF mean = 0
PDF variance = 0.11685
Sample size = 1000
Sample mean = 0.00239765
Sample variance = 0.116844
Sample maximum = 0.739647
Sample minimum = -0.742509
TEST006
For the Arcsin PDF:
ARCSIN_CDF evaluates the CDF;
ARCSIN_CDF_INV inverts the CDF.
ARCSIN_PDF evaluates the PDF;
PDF parameter A = 1
X PDF CDF CDF_INV
-0.773671 0.502393 0.218418 -0.773671
0.990598 2.32679 0.956318 0.990598
0.859956 0.623687 0.829509 0.859956
0.192611 0.324384 0.561695 0.192611
-0.262942 0.329919 0.415307 -0.262942
-0.978504 1.54349 0.0661187 -0.978504
-0.690074 0.439813 0.257578 -0.690074
-0.940927 0.940048 0.109957 -0.940927
-0.990535 2.31906 0.043829 -0.990535
0.408551 0.348743 0.633966 0.408551
TEST007
For the Arcsin PDF:
ARCSIN_MEAN computes the mean;
ARCSIN_SAMPLE samples;
ARCSIN_VARIANCE computes the variance.
PDF parameter A = 1
PDF mean = 0
PDF variance = 0.5
Sample size = 1000
Sample mean = 0.00986339
Sample variance = 0.490326
Sample maximum = 0.999978
Sample minimum = -0.999983
PDF parameter A = 16
PDF mean = 0
PDF variance = 128
Sample size = 1000
Sample mean = -0.453245
Sample variance = 129.51
Sample maximum = 15.9995
Sample minimum = -15.9993
TEST008
For the Benford PDF:
BENFORD_PDF evaluates the PDF.
N PDF(N)
1 0.30103
2 0.176091
3 0.124939
4 0.09691
5 0.0791812
6 0.0669468
7 0.0579919
8 0.0511525
9 0.0457575
10 0.0413927
11 0.0377886
12 0.0347621
13 0.0321847
14 0.0299632
15 0.0280287
16 0.0263289
17 0.0248236
18 0.0234811
19 0.0222764
TEST009
For the Bernoulli PDF,
BERNOULLI_CDF evaluates the CDF;
BERNOULLI_CDF_INV inverts the CDF;
BERNOULLI_PDF evaluates the PDF.
PDF parameter A = 0.75
X PDF CDF CDF_INV
0 0.25 0.25 0
1 0.75 1 1
1 0.75 1 1
1 0.75 1 1
1 0.75 1 1
0 0.25 0.25 0
1 0.75 1 1
0 0.25 0.25 0
0 0.25 0.25 0
1 0.75 1 1
TEST010
For the Bernoulli PDF:
BERNOULLI_MEAN computes the mean;
BERNOULLI_SAMPLE samples;
BERNOULLI_VARIANCE computes the variance.
PDF parameter A = 0.75
PDF mean = 0.75
PDF variance = 0.1875
Sample size = 1000
Sample mean = 0.768
Sample variance = 0.178354
Sample maximum = 1
Sample minimum = 0
TEST0105:
BESSEL_I0 evaluates the Bessel function of the
first kind and order 0;
BESSEL_I0_VALUES returns some exact values.
X Exact F BESSEL_I0(X)
0 1 1
0.2 1.01003 1.01003
0.4 1.0404 1.0404
0.6 1.09205 1.09205
0.8 1.16651 1.16651
1 1.26607 1.26607
1.2 1.39373 1.39373
1.4 1.5534 1.5534
1.6 1.74998 1.74998
1.8 1.98956 1.98956
2 2.27959 2.27959
2.5 3.28984 3.28984
3 4.88079 4.88079
3.5 7.3782 7.3782
4 11.3019 11.3019
4.5 17.4812 17.4812
5 27.2399 27.2399
6 67.2344 67.2344
8 427.564 427.564
10 2815.72 2815.72
TEST0106:
BESSEL_I1 evaluates the Bessel function of the
first kind and order 1;
BESSEL_I1_VALUES returns some exact values.
X Exact F BESSEL_I1(X)
0 0 0
0.2 0.100501 0.100501
0.4 0.204027 0.204027
0.6 0.313704 0.313704
0.8 0.432865 0.432865
1 0.565159 0.565159
1.2 0.714678 0.714678
1.4 0.886092 0.886092
1.6 1.08481 1.08481
1.8 1.31717 1.31717
2 1.59064 1.59064
2.5 2.51672 2.51672
3 3.95337 3.95337
3.5 6.20583 6.20583
4 9.75947 9.75947
4.5 15.3892 15.3892
5 24.3356 24.3356
6 61.3419 61.3419
8 399.873 399.873
10 2670.99 2670.99
TEST011
BETA evaluates the Beta function;
TGAMMA evaluates the Gamma function.
Argument A = 2.2
Argument B = 3.7
Beta(A,B) = 0.045376
(Expected value = 0.0454 )
Gamma(A)*Gamma(B)/Gamma(A+B) = 0.045376
TEST012
For the Beta PDF:
BETA_CDF evaluates the CDF;
BETA_CDF_INV inverts the CDF.
BETA_PDF evaluates the PDF;
PDF parameter A = 12
PDF parameter B = 12
A B X PDF CDF CDF_INV
12 12 0.678986 0.855881 0.963719 0.678986
12 12 0.401338 2.49915 0.166966 0.401337
12 12 0.635316 1.67553 0.909423 0.635317
12 12 0.594216 2.59905 0.821699 0.594216
12 12 0.504229 3.86528 0.516356 0.504229
12 12 0.802574 0.0256424 0.999472 0.802574
12 12 0.544908 3.53858 0.668704 0.544908
12 12 0.649115 1.38847 0.930537 0.649115
12 12 0.568142 3.14746 0.746604 0.568142
12 12 0.415317 2.80857 0.204083 0.415317
TEST013:
BETA_INC evaluates the normalized incomplete Beta
function BETA_INC(A,B,X).
BETA_INC_VALUES returns some exact values.
A B X Exact F BETA_INC(A,B,X)
0.5 0.5 0.01 0.0637686 0.0637686
0.5 0.5 0.1 0.204833 0.204833
0.5 0.5 1 1 1
1 0.5 0 0 0
1 0.5 0.01 0.00501256 0.00501256
1 0.5 0.1 0.0513167 0.0513167
1 0.5 0.5 0.292893 0.292893
1 1 0.5 0.5 0.5
2 2 0.1 0.028 0.028
2 2 0.2 0.104 0.104
2 2 0.3 0.216 0.216
2 2 0.4 0.352 0.352
2 2 0.5 0.5 0.5
2 2 0.6 0.648 0.648
2 2 0.7 0.784 0.784
2 2 0.8 0.896 0.896
2 2 0.9 0.972 0.972
5.5 5 0.5 0.436191 0.436191
10 0.5 0.9 0.151641 0.151641
10 5 0.5 0.0897827 0.0897827
10 5 1 1 1
10 10 0.5 0.5 0.5
20 5 0.8 0.459877 0.459877
20 10 0.6 0.214682 0.214682
20 10 0.8 0.950736 0.950736
20 20 0.5 0.5 0.5
20 20 0.6 0.897941 0.897941
30 10 0.7 0.22413 0.22413
30 10 0.8 0.758641 0.758641
40 20 0.7 0.700178 0.700178
1 0.5 0.1 0.0513167 0.0513167
1 0.5 0.2 0.105573 0.105573
1 0.5 0.3 0.16334 0.16334
1 0.5 0.4 0.225403 0.225403
1 2 0.2 0.36 0.36
1 3 0.2 0.488 0.488
1 4 0.2 0.5904 0.5904
1 5 0.2 0.67232 0.67232
2 2 0.3 0.216 0.216
3 2 0.3 0.0837 0.0837
4 2 0.3 0.03078 0.03078
5 2 0.3 0.010935 0.010935
1.30625 11.7562 0.225609 0.918885 0.918885
1.30625 11.7562 0.0335568 0.21053 0.21053
1.30625 11.7562 0.0295222 0.182413 0.182413
TEST014
For the Beta PDF:
BETA_MEAN computes the mean;
BETA_SAMPLE samples;
BETA_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 0.4
PDF variance = 0.04
Sample size = 1000
Sample mean = 0.406579
Sample variance = 0.0410724
Sample maximum = 0.942944
Sample minimum = 0.00629773
TEST015
For the Beta Binomial PDF:
BETA_BINOMIAL_CDF evaluates the CDF;
BETA_BINOMIAL_CDF_INV inverts the CDF.
BETA_BINOMIAL_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
PDF parameter C = 4
X PDF CDF CDF_INV
1 0.285714 0.5 1
4 0.0714286 1 4
3 0.171429 0.928571 3
2 0.257143 0.757143 2
1 0.285714 0.5 1
0 0.214286 0.214286 0
1 0.285714 0.5 1
0 0.214286 0.214286 0
0 0.214286 0.214286 0
2 0.257143 0.757143 2
TEST016
For the Beta Binomial PDF:
BETA_BINOMIAL_MEAN computes the mean;
BETA_BINOMIAL_SAMPLE samples;
BETA_BINOMIAL_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF parameter C = 4
PDF mean = 1.6
PDF variance = 1.44
Sample size = 1000
Sample mean = 1.62
Sample variance = 1.401
Sample maximum = 4
Sample minimum = 0
TEST020:
BINOMIAL_CDF evaluates the cumulative distribution
function for the discrete binomial probability
density function.
BINOMIAL_CDF_VALUES returns some exact values.
A is the number of trials;
B is the probability of success on one trial;
X is the number of successes;
BINOMIAL_CDF is the probability of having up to X
successes.
A B X Exact F BINOMIAL_CDF(A,B,X)
2 0.05 0 0.9025 0.9025
2 0.05 1 0.9975 0.9975
2 0.05 2 1 1
2 0.5 0 0.25 0.25
2 0.5 1 0.75 0.75
4 0.25 0 0.316406 0.316406
4 0.25 1 0.738281 0.738281
4 0.25 2 0.949219 0.949219
4 0.25 3 0.996094 0.996094
10 0.05 4 0.999936 0.999936
10 0.1 4 0.998365 0.998365
10 0.15 4 0.990126 0.990126
10 0.2 4 0.967207 0.967207
10 0.25 4 0.921873 0.921873
10 0.3 4 0.849732 0.849732
10 0.4 4 0.633103 0.633103
10 0.5 4 0.376953 0.376953
TEST021
For the Binomial PDF:
BINOMIAL_CDF evaluates the CDF;
BINOMIAL_CDF_INV inverts the CDF.
BINOMIAL_PDF evaluates the PDF;
PDF parameter A = 5
PDF parameter B = 0.65
X PDF CDF CDF_INV
3 0.336416 0.571585 3
5 0.116029 1 5
3 0.336416 0.571585 3
4 0.312386 0.883971 4
3 0.336416 0.571585 3
3 0.336416 0.571585 3
2 0.181147 0.235169 2
4 0.312386 0.883971 4
5 0.116029 1 5
2 0.181147 0.235169 2
TEST022
BINOMIAL_COEF evaluates binomial coefficients.
BINOMIAL_COEF_LOG evaluates the logarithm.
N K C(N,K)
0 0 1 1
1 0 1 1
1 1 1 1
2 0 1 1
2 1 2 2
2 2 1 1
3 0 1 1
3 1 3 3
3 2 3 3
3 3 1 1
4 0 1 1
4 1 4 4
4 2 6 6
4 3 4 4
4 4 1 1
TEST023
For the Binomial PDF:
BINOMIAL_MEAN computes the mean;
BINOMIAL_SAMPLE samples;
BINOMIAL_VARIANCE computes the variance;
PDF parameter A = 5
PDF parameter B = 0.3
PDF mean = 1.5
PDF variance = 1.05
Sample size = 1000
Sample mean = 1.522
Sample variance = 1.02854
Sample maximum = 5
Sample minimum = 0
TEST0235
For the Birthday PDF,
BIRTHDAY_CDF evaluates the CDF;
BIRTHDAY_CDF_INV inverts the CDF.
BIRTHDAY_PDF evaluates the PDF;
N PDF CDF CDF_INV
1 0 0 0
2 0.00273973 0.00273973 2
3 0.00546444 0.00820417 3
4 0.00815175 0.0163559 4
5 0.0107797 0.0271356 5
6 0.0133269 0.0404625 6
7 0.0157732 0.0562357 7
8 0.0180996 0.0743353 8
9 0.0202885 0.0946238 9
10 0.0223243 0.116948 10
11 0.0241932 0.141141 11
12 0.0258834 0.167025 12
13 0.0273855 0.19441 13
14 0.0286922 0.223103 14
15 0.0297988 0.252901 15
16 0.0307027 0.283604 16
17 0.0314037 0.315008 17
18 0.0319038 0.346911 18
19 0.0322071 0.379119 19
20 0.0323199 0.411438 20
21 0.03225 0.443688 21
22 0.032007 0.475695 22
23 0.0316019 0.507297 23
24 0.031047 0.538344 24
25 0.0303554 0.5687 25
26 0.0295411 0.598241 26
27 0.0286185 0.626859 27
28 0.0276022 0.654461 28
29 0.0265071 0.680969 29
30 0.0253477 0.706316 30
TEST024
For the Bradford PDF:
BRADFORD_CDF evaluates the CDF;
BRADFORD_CDF_INV inverts the CDF.
BRADFORD_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF CDF_INV
1.11788 1.59869 0.218418 1.11788
1.92165 0.574785 0.956318 1.92165
1.71934 0.685254 0.829509 1.71934
1.39286 0.993325 0.561695 1.39286
1.25948 1.21682 0.415307 1.25948
1.032 1.97451 0.0661187 1.032
1.14305 1.51422 0.257578 1.14305
1.05489 1.85808 0.109957 1.05489
1.02088 2.03647 0.043829 1.02088
1.46939 0.898629 0.633966 1.46939
TEST025
For the Bradford PDF:
BRADFORD_MEAN computes the mean;
BRADFORD_SAMPLE samples;
BRADFORD_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 1.38801
PDF variance = 0.0807807
Sample size = 1000
Sample mean = 1.3901
Sample variance = 0.0795644
Sample maximum = 1.99614
Sample minimum = 1.00085
TEST0251
BUFFON_LAPLACE_PDF evaluates the Buffon-Laplace PDF, the probability
that, on a grid of cells of width A and height B,
a needle of length L, dropped at random, will cross
at least one grid line.
A B L PDF
1 1 0 0
1 1 0.2 0.241916
1 1 0.4 0.458366
1 1 0.6 0.649352
1 1 0.8 0.814873
1 1 1 0.95493
1 2 0 0
1 2 0.2 0.18462
1 2 0.4 0.356507
1 2 0.6 0.515662
1 2 0.8 0.662085
1 2 1 0.795775
1 3 0 0
1 3 0.2 0.165521
1 3 0.4 0.322554
1 3 0.6 0.471099
1 3 0.8 0.611155
1 3 1 0.742723
1 4 0 0
1 4 0.2 0.155972
1 4 0.4 0.305577
1 4 0.6 0.448817
1 4 0.8 0.58569
1 4 1 0.716197
1 5 0 0
1 5 0.2 0.150242
1 5 0.4 0.295392
1 5 0.6 0.435448
1 5 0.8 0.570411
1 5 1 0.700282
2 1 0 0
2 1 0.2 0.18462
2 1 0.4 0.356507
2 1 0.6 0.515662
2 1 0.8 0.662085
2 1 1 0.795775
2 2 0 0
2 2 0.4 0.241916
2 2 0.8 0.458366
2 2 1.2 0.649352
2 2 1.6 0.814873
2 2 2 0.95493
2 3 0 0
2 3 0.4 0.203718
2 3 0.8 0.39046
2 3 1.2 0.560225
2 3 1.6 0.713014
2 3 2 0.848826
2 4 0 0
2 4 0.4 0.18462
2 4 0.8 0.356507
2 4 1.2 0.515662
2 4 1.6 0.662085
2 4 2 0.795775
2 5 0 0
2 5 0.4 0.173161
2 5 0.8 0.336135
2 5 1.2 0.488924
2 5 1.6 0.631527
2 5 2 0.763944
3 1 0 0
3 1 0.2 0.165521
3 1 0.4 0.322554
3 1 0.6 0.471099
3 1 0.8 0.611155
3 1 1 0.742723
3 2 0 0
3 2 0.4 0.203718
3 2 0.8 0.39046
3 2 1.2 0.560225
3 2 1.6 0.713014
3 2 2 0.848826
3 3 0 0
3 3 0.6 0.241916
3 3 1.2 0.458366
3 3 1.8 0.649352
3 3 2.4 0.814873
3 3 3 0.95493
3 4 0 0
3 4 0.6 0.213268
3 4 1.2 0.407437
3 4 1.8 0.582507
3 4 2.4 0.738479
3 4 3 0.875352
3 5 0 0
3 5 0.6 0.196079
3 5 1.2 0.376879
3 5 1.8 0.5424
3 5 2.4 0.692642
3 5 3 0.827606
4 1 0 0
4 1 0.2 0.155972
4 1 0.4 0.305577
4 1 0.6 0.448817
4 1 0.8 0.58569
4 1 1 0.716197
4 2 0 0
4 2 0.4 0.18462
4 2 0.8 0.356507
4 2 1.2 0.515662
4 2 1.6 0.662085
4 2 2 0.795775
4 3 0 0
4 3 0.6 0.213268
4 3 1.2 0.407437
4 3 1.8 0.582507
4 3 2.4 0.738479
4 3 3 0.875352
4 4 0 0
4 4 0.8 0.241916
4 4 1.6 0.458366
4 4 2.4 0.649352
4 4 3.2 0.814873
4 4 4 0.95493
4 5 0 0
4 5 0.8 0.218997
4 5 1.6 0.417623
4 5 2.4 0.595876
4 5 3.2 0.753758
4 5 4 0.891268
5 1 0 0
5 1 0.2 0.150242
5 1 0.4 0.295392
5 1 0.6 0.435448
5 1 0.8 0.570411
5 1 1 0.700282
5 2 0 0
5 2 0.4 0.173161
5 2 0.8 0.336135
5 2 1.2 0.488924
5 2 1.6 0.631527
5 2 2 0.763944
5 3 0 0
5 3 0.6 0.196079
5 3 1.2 0.376879
5 3 1.8 0.5424
5 3 2.4 0.692642
5 3 3 0.827606
5 4 0 0
5 4 0.8 0.218997
5 4 1.6 0.417623
5 4 2.4 0.595876
5 4 3.2 0.753758
5 4 4 0.891268
5 5 0 0
5 5 1 0.241916
5 5 2 0.458366
5 5 3 0.649352
5 5 4 0.814873
5 5 5 0.95493
TEST0252
BUFFON_LAPLACE_SIMULATE simulates a Buffon-Laplace needle dropping
experiment. On a grid of cells of width A and height B,
a needle of length L is dropped at random. We count
the number of times it crosses at least one grid line,
and use this to estimate the value of PI.
Cell width A = 1
Cell height B = 1
Needle length L = 1
Trials Hits Est(Pi) Err
10 10 3 0.141593
100 98 3.06122 0.0803682
10000 9557 3.13906 0.00253228
1000000 954728 3.14226 0.00066357
TEST0253
BUFFON_PDF evaluates the Buffon PDF, the probability
that, on a grid of cells of width A,
a needle of length L, dropped at random, will cross
at least one grid line.
A L PDF
1 0 0
1 0.2 0.127324
1 0.4 0.254648
1 0.6 0.381972
1 0.8 0.509296
1 1 0.63662
2 0 0
2 0.4 0.127324
2 0.8 0.254648
2 1.2 0.381972
2 1.6 0.509296
2 2 0.63662
3 0 0
3 0.6 0.127324
3 1.2 0.254648
3 1.8 0.381972
3 2.4 0.509296
3 3 0.63662
4 0 0
4 0.8 0.127324
4 1.6 0.254648
4 2.4 0.381972
4 3.2 0.509296
4 4 0.63662
5 0 0
5 1 0.127324
5 2 0.254648
5 3 0.381972
5 4 0.509296
5 5 0.63662
TEST0254
BUFFON_SIMULATE simulates a Buffon needle dropping
experiment. On a grid of cells of width A,
a needle of length L is dropped at random. We count
the number of times it crosses at least one grid line,
and use this to estimate the value of PI.
Cell width A = 1
Needle length L = 1
Trials Hits Est(Pi) Err
10 4 5 1.85841
100 73 2.73973 0.401867
10000 6389 3.13038 0.0112123
1000000 637013 3.13965 0.0019393
TEST026
For the Burr PDF:
BURR_CDF evaluates the CDF;
BURR_CDF_INV inverts the CDF.
BURR_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF parameter D = 2
X PDF CDF CDF_INV
2.91469 0.364571 0.218418 2.91469
8.07561 0.0179097 0.956318 8.07561
5.33847 0.102359 0.829509 5.33847
3.88175 0.292999 0.561695 3.88175
3.4385 0.363335 0.415307 3.4385
2.40426 0.209864 0.0661187 2.40426
3.02016 0.376757 0.257578 3.02016
2.58327 0.278521 0.109957 2.58327
2.28429 0.161895 0.043829 2.28429
4.15007 0.24607 0.633966 4.15007
TEST027
For the Burr PDF:
BURR_MEAN computes the mean;
BURR_SAMPLE samples;
BURR_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF parameter D = 2
PDF mean = 4.22453
PDF variance = 5.72505
Sample size = 1000
Sample mean = 4.21466
Sample variance = 4.28559
Sample maximum = 20.6931
Sample minimum = 1.71031
TEST0275
For the Cardioid PDF:
CARDIOID_CDF evaluates the CDF;
CARDIOID_CDF_INV inverts the CDF.
CARDIOID_PDF evaluates the PDF;
PDF parameter A = 0
PDF parameter B = 0.25
X PDF CDF CDF_INV
-1.28896 0.181287 0.218419 -1.28895
2.61646 0.0902998 0.956317 2.61646
1.57037 0.159189 0.829509 1.57037
0.259396 0.23607 0.561695 0.259396
-0.357278 0.233707 0.415307 -0.357278
-2.38175 0.101466 0.0661188 -2.38175
-1.08178 0.196537 0.257578 -1.08178
-1.99504 0.126398 0.109957 -1.99504
-2.61484 0.0903646 0.0438293 -2.61484
0.571348 0.226093 0.633966 0.571348
TEST0276
For the Cardioid PDF:
CARDIOID_MEAN computes the mean;
CARDIOID_SAMPLE samples;
CARDIOID_VARIANCE computes the variance.
PDF parameter A = 0
PDF parameter B = 0.25
PDF mean = 0
PDF variance = 0
Sample size = 1000
Sample mean = 0.00991354
Sample variance = 2.28985
Sample maximum = 3.11531
Sample minimum = -3.11849
TEST028
For the Cauchy PDF:
CAUCHY_CDF evaluates the CDF;
CAUCHY_CDF_INV inverts the CDF.
CAUCHY_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
-1.66329 0.0425934 0.218418 -1.66329
23.7233 0.0019857 0.956318 23.7233
7.05492 0.0276373 0.829509 7.05492
2.58886 0.102167 0.561695 2.58886
1.1824 0.0987675 0.415307 1.1824
-12.2343 0.00451256 0.0661187 -12.2343
-0.860458 0.0555766 0.257578 -0.860458
-6.33637 0.0121655 0.109957 -6.33637
-19.6498 0.00199897 0.043829 -19.6498
3.34283 0.0883932 0.633966 3.34283
TEST029
For the Cauchy PDF:
CAUCHY_MEAN computes the mean;
CAUCHY_SAMPLE samples;
CAUCHY_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 2
PDF variance = inf
Sample size = 1000
Sample mean = 1.66442
Sample variance = 1579.41
Sample maximum = 458.532
Sample minimum = -517.438
TEST030
For the Chi PDF:
CHI_CDF evaluates the CDF;
CHI_CDF_INV inverts the CDF.
CHI_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF CDF_INV
5.29456 0.183427 0.797383 5.29492
7.13704 0.0338961 0.975756 7.13672
2.45642 0.162283 0.0878118 2.45703
6.98388 0.040642 0.97006 6.98438
4.74497 0.242317 0.680042 4.74512
3.0281 0.245322 0.205594 3.02832
2.7946 0.214758 0.151764 2.79492
2.95034 0.235816 0.186883 2.9502
2.49461 0.168514 0.0941283 2.49414
2.35125 0.144944 0.0716542 2.35156
TEST031
For the Chi PDF:
CHI_MEAN computes the mean;
CHI_SAMPLE samples;
CHI_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 4.19154
PDF variance = 1.81408
Sample size = 1000
Sample mean = 4.15337
Sample variance = 1.9332
Sample maximum = 9.32689
Sample minimum = 1.20601
TEST032:
CHI_SQUARE_CDF evaluates the cumulative
distribution function for the chi-square central
probability density function.
CHI_SQUARE_CDF_VALUES returns some exact values.
A X Exact F CHI_SQUARE_CDF(A,X)
1 0.01 0.0796557 0.0796557
2 0.01 0.00498752 0.00498752
1 0.02 0.112463 0.112463
2 0.02 0.00995017 0.00995017
1 0.4 0.472911 0.472911
2 0.4 0.181269 0.181269
3 0.4 0.0597575 0.0597575
4 0.4 0.0175231 0.0175231
1 1 0.682689 0.682689
2 1 0.393469 0.393469
3 1 0.198748 0.198748
4 1 0.090204 0.090204
5 1 0.0374342 0.0374342
3 2 0.427593 0.427593
3 3 0.608375 0.608375
3 4 0.738536 0.738536
3 5 0.828203 0.828203
3 6 0.88839 0.88839
10 1 0.000172116 0.000172116
10 2 0.00365985 0.00365985
10 3 0.0185759 0.0185759
TEST033
For the Chi Square PDF:
CHI_SQUARE_CDF evaluates the CDF;
CHI_SQUARE_CDF_INV inverts the CDF.
CHI_SQUARE_PDF evaluates the PDF;
PDF parameter A = 4
X PDF CDF CDF_INV
6.22214 0.0693042 0.816838 6.22214
8.25908 0.0332227 0.917464 8.25908
9.02741 0.0247301 0.939582 9.02741
4.13727 0.130694 0.612253 4.13727
0.703353 0.123704 0.0490852 0.703353
1.44998 0.175567 0.164536 1.44998
0.634817 0.115542 0.0408827 0.634817
8.54272 0.02982 0.926397 8.54272
13.0901 0.00470332 0.989156 13.0901
1.46095 0.175928 0.166465 1.46095
TEST034
For the Chi Square PDF:
CHI_SQUARE_MEAN computes the mean;
CHI_SQUARE_SAMPLE samples;
CHI_SQUARE_VARIANCE computes the variance.
PDF parameter A = 10
PDF mean = 10
PDF variance = 20
Sample size = 1000
Sample mean = 9.97738
Sample variance = 21.1882
Sample maximum = 31.1387
Sample minimum = 1.63719
TEST035
For the Chi Square Noncentral PDF:
CHI_SQUARE_NONCENTRAL_MEAN computes the mean;
CHI_SQUARE_NONCENTRAL_SAMPLE samples;
CHI_SQUARE_NONCENTRAL_VARIANCE computes the variance;
PDF parameter A = 3
PDF parameter B = 2
PDF mean = 5
PDF variance = 14
Initial seed = 123456789
Final seed = 200382020
Sample size = 1000
Sample mean = 4.99931
Sample variance = 13.5745
Sample maximum = 22.5373
Sample minimum = 0.0271069
TEST036
For the Circle PDF:
CIRCLE_SAMPLE samples;
PDF parameter A = 10
PDF parameter B = 4
PDF parameter C = 3
Sample size = 1000
Sample mean = 9.99926 4.06034
Sample variance = 2.28924 2.19259
Sample maximum = 12.9218 6.96697
Sample minimum = 7.04381 1.03574
TEST037
For the Circular Normal 01 PDF:
CIRCULAR_NORMAL_01_MEAN computes the mean;
CIRCULAR_NORMAL_01_SAMPLE samples;
CIRCULAR_NORMAL_01_VARIANCE computes the variance.
PDF mean = 0 0
PDF variance = 1 1
Sample size = 1000
Sample mean = 0.00581875 0.0215871
Sample variance = 0.998375 1.00517
Sample maximum = 3.32858 3.02853
Sample minimum = -3.02975 -2.90483
TEST0375
For the Circular Normal PDF:
CIRCULAR_NORMAL_MEAN computes the mean;
CIRCULAR_NORMAL_SAMPLE samples;
CIRCULAR_NORMAL_VARIANCE computes the variance.
PDF mean = 1 5
PDF variance = 0.75 0.75
Sample size = 1000
Sample mean = 1.00436 5.01619
Sample variance = 0.561586 0.565407
Sample maximum = 3.49644 7.2714
Sample minimum = -1.27232 2.82138
TEST038
For the Cosine PDF:
COSINE_CDF evaluates the CDF;
COSINE_CDF_INV inverts the CDF.
COSINE_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 1
X PDF CDF CDF_INV
1.04663 0.0921411 0.218496 1.04663
3.93128 -0.0561385 0.956298 3.93128
3.15509 0.0642729 0.829438 3.15509
2.19443 0.156156 0.561695 2.19443
1.73232 0.153487 0.415302 1.73232
0.258932 -0.0269689 0.066047 0.258932
1.19619 0.110449 0.257478 1.19619
0.542718 0.0180276 0.109936 0.542718
0.0702522 -0.05591 0.0438598 0.0702522
2.42721 0.144851 0.633937 2.42721
TEST039
For the Cosine PDF:
COSINE_MEAN computes the mean;
COSINE_SAMPLE samples;
COSINE_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 1
PDF mean = 2
PDF variance = 1.28987
Sample size = 1000
Sample mean = 2.00654
Sample variance = 1.29547
Sample maximum = 4.71208
Sample minimum = -0.72435
TEST0395
COUPON_COMPLETE_PDF evaluates the coupon collector's
complete collection pdf.
Number of coupon types is 2
BOX_NUM PDF CDF
1 0 0
2 0.5 0.5
3 0.25 0.75
4 0.125 0.875
5 0.0625 0.9375
6 0.03125 0.96875
7 0.015625 0.984375
8 0.0078125 0.992188
9 0.00390625 0.996094
10 0.00195312 0.998047
11 0.000976562 0.999023
12 0.000488281 0.999512
13 0.000244141 0.999756
14 0.00012207 0.999878
15 6.10352e-05 0.999939
16 3.05176e-05 0.999969
17 1.52588e-05 0.999985
18 7.62939e-06 0.999992
19 3.8147e-06 0.999996
20 1.90735e-06 0.999998
Number of coupon types is 3
BOX_NUM PDF CDF
1 0 0
2 0 0
3 0.222222 0.222222
4 0.222222 0.444444
5 0.17284 0.617284
6 0.123457 0.740741
7 0.085048 0.825789
8 0.0576132 0.883402
9 0.0387136 0.922116
10 0.0259107 0.948026
11 0.0173077 0.965334
12 0.0115497 0.976884
13 0.00770358 0.984587
14 0.00513698 0.989724
15 0.00342507 0.993149
16 0.00228352 0.995433
17 0.00152239 0.996955
18 0.00101494 0.99797
19 0.000676634 0.998647
20 0.000451091 0.999098
Number of coupon types is 4
BOX_NUM PDF CDF
1 0 0
2 0 0
3 0 0
4 0.09375 0.09375
5 0.140625 0.234375
6 0.146484 0.380859
7 0.131836 0.512695
8 0.110229 0.622925
9 0.0884399 0.711365
10 0.0692368 0.780602
11 0.0533867 0.833988
12 0.040771 0.874759
13 0.0309441 0.905703
14 0.0233911 0.929094
15 0.0176349 0.946729
16 0.0132719 0.960001
17 0.00997682 0.969978
18 0.00749406 0.977472
19 0.00562627 0.983098
20 0.00422256 0.987321
TEST040:
COUPON_SIMULATE simulates the couponn collector's problem.
Number of coupon types is 5
Expected wait is about 8.04719
1 10
2 8
3 14
4 7
5 10
6 11
7 17
8 11
9 6
10 12
Average wait was 10.6
Number of coupon types is 10
Expected wait is about 23.0259
1 29
2 31
3 47
4 42
5 27
6 31
7 44
8 23
9 11
10 30
Average wait was 31.5
Number of coupon types is 15
Expected wait is about 40.6208
1 65
2 31
3 60
4 51
5 46
6 37
7 51
8 40
9 52
10 52
Average wait was 48.5
Number of coupon types is 20
Expected wait is about 59.9146
1 80
2 80
3 51
4 54
5 58
6 80
7 173
8 69
9 156
10 54
Average wait was 85.5
Number of coupon types is 25
Expected wait is about 80.4719
1 117
2 188
3 95
4 77
5 168
6 110
7 128
8 77
9 103
10 82
Average wait was 114.5
TEST041
For the Deranged PDF:
DERANGED_CDF evaluates the CDF;
DERANGED_CDF_INV inverts the CDF.
DERANGED_PDF evaluates the PDF;
PDF parameter A = 7
X PDF CDF CDF_INV
0 0.367857 0.367857 0
3 0.0625 0.981746 3
2 0.183333 0.919246 2
1 0.368056 0.735913 1
1 0.368056 0.735913 1
0 0.367857 0.367857 0
0 0.367857 0.367857 0
0 0.367857 0.367857 0
0 0.367857 0.367857 0
1 0.368056 0.735913 1
TEST042
For the Deranged PDF:
DERANGED_CDF evaluates the CDF;
DERANGED_PDF evaluates the PDF;
PDF parameter A = 7
X PDF CDF
0 0.367857 0.367857
1 0.368056 0.735913
2 0.183333 0.919246
3 0.0625 0.981746
4 0.0138889 0.995635
5 0.00416667 0.999802
6 0 0.999802
7 0.000198413 1
TEST043
For the Deranged PDF:
DERANGED_MEAN computes the mean;
DERANGED_SAMPLE samples;
DERANGED_VARIANCE computes the variance.
PDF parameter A = 7
PDF mean = 1
PDF variance = 0.632143
Sample size = 1000
Sample mean = 1.004
Sample variance = 0.984969
Sample maximum = 5
Sample minimum = 0
TEST044:
DIGAMMA evaluates the DIGAMMA or PSI function.
PSI_VALUES returns some exact values.
X Exact F DIGAMMA(X)
0.1 -10.4238 -10.4238
0.2 -5.28904 -5.28904
0.3 -3.50252 -3.50252
0.4 -2.56138 -2.56138
0.5 -1.96351 -1.96351
0.6 -1.54062 -1.54062
0.7 -1.22002 -1.22002
0.8 -0.965009 -0.965009
0.9 -0.754927 -0.754927
1 -0.577216 -0.577216
1.1 -0.423755 -0.423755
1.2 -0.28904 -0.28904
1.3 -0.169191 -0.169191
1.4 -0.0613845 -0.0613845
1.5 0.03649 0.03649
1.6 0.126047 0.126047
1.7 0.208548 0.208548
1.8 0.284991 0.284991
1.9 0.356184 0.356184
2 0.422784 0.422784
TEST045
For the Cosine PDF:
DIPOLE_CDF evaluates the CDF;
DIPOLE_CDF_INV inverts the CDF.
DIPOLE_PDF evaluates the PDF;
PDF parameter A = 0
PDF parameter B = 1
X PDF CDF CDF_INV
0.515107 0.573233 0.780988 0.515137
-1.28591 0.153127 0.056141 -1.28516
0.467924 0.589867 0.761502 0.467773
0.295557 0.627128 0.677995 0.29541
-0.16527 0.635573 0.396656 -0.165283
-0.219095 0.63352 0.364799 -0.219238
0.0507089 0.63661 0.532227 0.0507812
0.883735 0.374656 0.888326 0.883789
-0.317761 0.624268 0.310195 -0.317871
0.298513 0.626776 0.679584 0.29834
PDF parameter A = 0.785398
PDF parameter B = 0.5
X PDF CDF CDF_INV
-2.00376 0.0538127 0.131477 -2.00293
1.90221 0.060188 0.828708 1.90332
9.07094 0.00368677 0.964094 9.09375
0.244458 0.316631 0.501226 0.244629
0.203988 0.317466 0.487654 0.204102
-10.6175 0.00288846 0.029192 -10.6211
-0.86502 0.226546 0.227479 -0.865234
2.15741 0.0463925 0.847767 2.15674
-4.81123 0.0129237 0.0619356 -4.81836
0.646407 0.273715 0.626535 0.646484
PDF parameter A = 1.5708
PDF parameter B = 0
X PDF CDF CDF_INV
-0.904508 0.175075 0.265947 -0.904297
-0.843581 0.185969 0.276943 -0.84375
0.227018 0.302709 0.571058 0.227051
-0.320266 0.288698 0.401342 -0.320312
-0.506838 0.253253 0.35068 -0.506836
0.251535 0.299369 0.578439 0.251465
-0.177728 0.308563 0.444012 -0.177734
-0.386329 0.276972 0.38265 -0.38623
-0.0852594 0.316013 0.472927 -0.0849609
-1.51135 0.0969218 0.186061 -1.51074
TEST046
For the Cosine PDF:
DIPOLE_SAMPLE samples;
PDF parameter A = 0
PDF parameter B = 1
Sample size = 1000
Sample mean = 0.017141
Sample variance = 0.728062
Sample maximum = 4.78718
Sample minimum = -5.67547
PDF parameter A = 0.785398
PDF parameter B = 0.5
Sample size = 1000
Sample mean = 0.28364
Sample variance = 252.082
Sample maximum = 245.982
Sample minimum = -245.584
PDF parameter A = 1.5708
PDF parameter B = 0
Sample size = 1000
Sample mean = -0.179305
Sample variance = 242.215
Sample maximum = 119.648
Sample minimum = -335.78
TEST047
For the Dirichlet PDF:
DIRICHLET_MEAN computes the mean;
DIRICHLET_SAMPLE samples;
DIRICHLET_VARIANCE computes the variance;
Number of components N = 3
PDF parameter A:
1 0.25
2 0.5
3 1.25
PDF mean:
1 0.125
2 0.25
3 0.625
PDF variance:
1 0.0364583
2 0.0625
3 0.078125
Second moment matrix:
Col: 1 2 3
Row
---
1 0.0520833 0.0208333 0.0520833
2 0.0208333 0.125 0.104167
3 0.0520833 0.104167 0.46875
Sample size = 1000
Component Mean, Variance, Min, Max:
0 0.128337 0.0377062 0.975128 4.0796e-11
1 0.23718 0.0592189 0.976032 1.30377e-06
2 0.634483 0.0751289 0.999945 0.000245466
TEST048
For the Dirichlet PDF:
DIRICHLET_PDF evaluates the PDF;
Number of components N = 3
PDF parameter A:
1 0.25
2 0.5
3 1.25
PDF argument X:
1 0.5
2 0.125
3 0.375
PDF value = 0.63907
TEST049
For the Dirichlet Mixture PDF:
DIRICHLET_MIX_SAMPLE samples;
DIRICHLET_MIX_MEAN computes the mean;
Number of elements ELEM_NUM = 3
Number of components COMP_NUM = 2
PDF parameters A(ELEM,COMP):
Col: 1 2
Row
---
1 0.25 1.5
2 0.5 0.5
3 1.25 2
Component weights
1 1
2 2
PDF mean
1 0.291667
2 0.166667
3 0.541667
Sample size = 1000
Component Mean, Variance, Max, Min:
0 0.278716 0.0546592 0.986951 3.62858e-10
1 0.170222 0.0397946 0.993637 5.84186e-08
2 0.551062 0.062022 0.998934 0.00518575
TEST050
For the Dirichlet mixture PDF:
DIRICHLET_MIX_PDF evaluates the PDF.
Number of elements ELEM_NUM = 3
Number of components COMP_NUM = 2
PDF parameters A(ELEM,COMP):
Col: 1 2
Row
---
1 0.25 1.5
2 0.5 0.5
3 1.25 2
Component weights
1 1
2 2
PDF argument X:
1 0.5
2 0.125
3 0.375
PDF value = 2.12288
TEST051
BETA_PDF evaluates the Beta PDF.
DIRICHLET_PDF evaluates the Dirichlet PDF.
For N = 2, Dirichlet = Beta.
Number of components N = 2
PDF parameters A(1:N):
1 2.5
2 3.5
PDF arguments X(1:N):
1 0.25
2 0.75
Dirichlet PDF value = 1.65399
Beta PDF value = 1.65399
TEST052
For the Discrete PDF:
DISCRETE_CDF evaluates the CDF;
DISCRETE_CDF_INV inverts the CDF.
DISCRETE_PDF evaluates the PDF;
PDF parameter A = 6
PDF parameter B:
1 1
2 2
3 6
4 2
5 4
6 1
X PDF CDF CDF_INV
3 0.375 0.5625 3
6 0.0625 1 6
5 0.25 0.9375 5
3 0.375 0.5625 3
3 0.375 0.5625 3
2 0.125 0.1875 2
3 0.375 0.5625 3
2 0.125 0.1875 2
1 0.0625 0.0625 1
4 0.125 0.6875 4
TEST053
For the Discrete PDF:
DISCRETE_MEAN computes the mean;
DISCRETE_SAMPLE samples;
DISCRETE_VARIANCE computes the variance;
PDF parameter A = 6
PDF parameter B:
1 1
2 2
3 6
4 2
5 4
6 1
PDF mean = 3.5625
PDF variance = 1.74609
Sample size = 1000
Sample mean = 3.559
Sample variance = 1.73826
Sample maximum = 6
Sample minimum = 1
TEST054
For the Empirical Discrete PDF:
EMPIRICAL_DISCRETE_CDF evaluates the CDF;
EMPIRICAL_DISCRETE_CDF_INV inverts the CDF.
EMPIRICAL_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 6
PDF parameter B =
1 1
2 1
3 3
4 2
5 1
6 2
PDF parameter C =
1 0
2 1
3 2
4 4.5
5 6
6 10
X PDF CDF CDF_INV
2 0.3 0.5 2
10 0.2 1 10
10 0.2 1 10
4.5 0.2 0.7 4.5
2 0.3 0.5 2
0 0.1 0.1 0
2 0.3 0.5 2
1 0.1 0.2 1
0 0.1 0.1 0
4.5 0.2 0.7 4.5
TEST055
For the Empirical Discrete PDF:
EMPIRICAL_DISCRETE_MEAN computes the mean;
EMPIRICAL_DISCRETE_SAMPLE samples;
EMPIRICAL_DISCRETE_VARIANCE computes the variance.
PDF parameter A = 6
PDF parameter B =
1 1
2 1
3 3
4 2
5 1
6 2
PDF parameter C =
1 0
2 1
3 2
4 4.5
5 6
6 10
PDF mean = 4.2
PDF variance = 11.31
Sample size = 1000
Sample mean = 4.231
Sample variance = 11.2023
Sample maximum = 10
Sample minimum = 0
TEST056
For the Empirical Discrete PDF:
EMPIRICAL_DISCRETE_CDF evaluates the CDF;
EMPIRICAL_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 6
PDF parameter B =
1 1
2 1
3 3
4 2
5 1
6 2
PDF parameter C =
1 0
2 1
3 2
4 4.5
5 6
6 10
X PDF CDF
-2 0 0
-1 0 0
0 0.1 0.1
1 0.1 0.2
2 0.3 0.5
3 0 0.5
4 0 0.5
5 0 0.7
6 0.1 0.8
7 0 0.8
8 0 0.8
9 0 0.8
10 0.2 1
11 0 1
12 0 1
TEST0563
For the English Sentence Length PDF:
ENGLISH_SENTENCE_LENGTH_CDF evaluates the CDF;
ENGLISH_SENTENCE_LENGTH_CDF_INV inverts the CDF.
ENGLISH_SENTENCE_LENGTH_PDF evaluates the PDF;
X PDF CDF CDF_INV
9 0.0329364 0.232179 9
43 0.00478109 0.957141 43
30 0.0155962 0.840951 30
19 0.0333674 0.587303 19
14 0.0375972 0.415634 14
5 0.0305008 0.0965039 5
10 0.0354122 0.267591 10
6 0.0319642 0.128468 6
4 0.0255292 0.0660031 4
21 0.0287367 0.647141 21
TEST0564
For the English Sentence Length PDF:
ENGLISH_SENTENCE_LENGTH_MEAN computes the mean;
ENGLISH_SENTENCE_LENGTH_SAMPLE samples;
ENGLISH_SENTENCE_LENGTH_VARIANCE computes the variance.
PDF mean = 19.1147
PDF variance = 147.443
Sample size = 1000
Sample mean = 19.107
Sample variance = 144.238
Sample maximum = 67
Sample minimum = 1
TEST0565
For the English Word Length PDF:
ENGLISH_WORD_LENGTH_CDF evaluates the CDF;
ENGLISH_WORD_LENGTH_CDF_INV inverts the CDF.
ENGLISH_WORD_LENGTH_PDF evaluates the PDF;
X PDF CDF CDF_INV
3 0.211926 0.413282 3
10 0.0276608 0.965289 10
7 0.0772423 0.841075 7
4 0.156785 0.570067 4
4 0.156785 0.570067 4
2 0.169755 0.201356 2
3 0.211926 0.413282 3
2 0.169755 0.201356 2
2 0.169755 0.201356 2
5 0.108523 0.67859 5
TEST0566
For the English Word Length PDF:
ENGLISH_WORD_LENGTH_MEAN computes the mean;
ENGLISH_WORD_LENGTH_SAMPLE samples;
ENGLISH_WORD_LENGTH_VARIANCE computes the variance.
PDF mean = 4.73912
PDF variance = 7.05635
Sample size = 1000
Sample mean = 4.74
Sample variance = 6.96737
Sample maximum = 15
Sample minimum = 1
TEST057
For the Erlang PDF:
ERLANG_CDF evaluates the CDF;
ERLANG_CDF_INV inverts the CDF.
ERLANG_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF CDF_INV
11.2926 0.0385403 0.887143 11.293
3.85983 0.122337 0.173777 3.85938
1.91828 0.0332989 0.0114788 1.91797
4.33148 0.131139 0.233762 4.33203
8.02827 0.0919195 0.681759 8.02734
6.42343 0.122108 0.50924 6.42383
5.14542 0.135161 0.342996 5.14551
4.9536 0.135317 0.317044 4.95312
6.71621 0.117176 0.544281 6.7168
5.9501 0.128886 0.449771 5.9502
TEST058
For the Erlang PDF:
ERLANG_MEAN computes the mean;
ERLANG_SAMPLE samples;
ERLANG_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 7
PDF variance = 12
Sample size = 1000
Sample mean = 7.00341
Sample variance = 11.491
Sample maximum = 21.5166
Sample minimum = 1.22651
TEST059
ERROR_F evaluates ERF(X).
ERROR_F_INVERSE inverts ERF(X).
X -> Y = error_F(X) -> Z = error_f_inverse(Y)
1.67904 0.982428 1.67904
-0.56606 -0.576596 -0.56606
1.21293 0.913719 1.21293
1.26938 0.927374 1.26938
-1.66609 -0.981537 -1.66609
-2.24246 -0.998483 -2.24246
0.0396749 0.0447449 0.0396749
0.673068 0.658833 0.673068
-0.275127 -0.30279 -0.275127
2.164 0.997789 2.164
0.297785 0.326341 0.297785
2.04454 0.996165 2.04454
1.39882 0.952097 1.39882
-1.24299 -0.921226 -1.24299
-0.0670837 -0.0755824 -0.0670837
-0.794396 -0.738752 -0.794396
-0.523768 -0.541137 -0.523768
-0.350567 -0.379948 -0.350567
0.1317 0.147753 0.1317
0.53738 0.552727 0.53738
TEST060
For the Exponential 01 PDF:
EXPONENTIAL_01_CDF evaluates the CDF;
EXPONENTIAL_01_CDF_INV inverts the CDF.
EXPONENTIAL_01_PDF evaluates the PDF;
X PDF CDF CDF_INV
0.246436 0.781582 0.218418 0.246436
3.13081 0.0436824 0.956318 3.13081
1.76907 0.170491 0.829509 1.76907
0.824841 0.438305 0.561695 0.824841
0.536668 0.584693 0.415307 0.536668
0.068406 0.933881 0.0661187 0.068406
0.297837 0.742422 0.257578 0.297837
0.116485 0.890043 0.109957 0.116485
0.0448185 0.956171 0.043829 0.0448185
1.00503 0.366034 0.633966 1.00503
TEST061
For the Exponential 01 PDF:
EXPONENTIAL_01_MEAN computes the mean;
EXPONENTIAL_01_SAMPLE samples;
EXPONENTIAL_01_VARIANCE computes the variance.
PDF mean = 1
PDF variance = 1
Sample size = 1000
Sample mean = 1.00328
Sample variance = 0.981133
Sample maximum = 6.16979
Sample minimum = 0.00184006
TEST062
For the Exponential PDF:
EXPONENTIAL_CDF evaluates the CDF;
EXPONENTIAL_CDF_INV inverts the CDF.
EXPONENTIAL_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
X PDF CDF CDF_INV
1.49287 0.390791 0.218418 1.49287
7.26162 0.0218412 0.956318 7.26162
4.53815 0.0852454 0.829509 4.53815
2.64968 0.219152 0.561695 2.64968
2.07334 0.292346 0.415307 2.07334
1.13681 0.466941 0.0661187 1.13681
1.59567 0.371211 0.257578 1.59567
1.23297 0.445022 0.109957 1.23297
1.08964 0.478086 0.043829 1.08964
3.01006 0.183017 0.633966 3.01006
TEST063
For the Exponential PDF:
EXPONENTIAL_MEAN computes the mean;
EXPONENTIAL_SAMPLE samples;
EXPONENTIAL_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 10
PDF mean = 11
PDF variance = 100
Sample size = 1000
Sample mean = 11.0328
Sample variance = 98.1133
Sample maximum = 62.6979
Sample minimum = 1.0184
TEST064
For the Extreme Values PDF:
EXTREME_VALUES_CDF evaluates the CDF;
EXTREME_VALUES_CDF_INV inverts the CDF.
EXTREME_VALUES_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
0.741219 0.110763 0.218418 0.741219
11.3257 0.014238 0.956318 11.3257
7.03121 0.0516842 0.829509 7.03121
3.6508 0.107994 0.561695 3.6508
2.38781 0.121649 0.415307 2.38781
-0.997815 0.0598662 0.0661187 -0.997815
1.08542 0.116462 0.257578 1.08542
-0.37581 0.080916 0.109957 -0.37581
-1.42066 0.0456911 0.043829 -1.42066
4.35736 0.0963122 0.633966 4.35736
TEST065
For the Extreme Values PDF:
EXTREME_VALUES_MEAN computes the mean;
EXTREME_VALUES_SAMPLE samples;
EXTREME_VALUES_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 3.73165
PDF variance = 14.8044
Sample size = 1000
Sample mean = 3.74498
Sample variance = 14.6723
Sample maximum = 20.5062
Sample minimum = -3.52111
TEST066:
F_CDF evaluates the cumulative
distribution function for the F
probability density function.
F_CDF_VALUES returns some exact values.
A B X Exact F F_CDF(A,B,X)
1 1 1 0.5 0.5
1 5 0.528 0.499971 0.499971
5 1 1.89 0.499603 0.499603
1 5 1.69 0.749699 0.749699
2 10 1.6 0.750466 0.750466
4 20 1.47 0.751416 0.751416
1 5 4.06 0.899987 0.899987
6 6 3.05 0.899713 0.899713
8 16 2.09 0.900285 0.900285
1 5 6.61 0.950025 0.950025
3 10 3.71 0.950057 0.950057
6 12 3 0.950193 0.950193
1 5 10.01 0.975013 0.975013
1 5 16.26 0.990002 0.990002
1 5 22.78 0.994998 0.994998
1 5 47.18 0.999 0.999
2 5 1 0.568799 0.568799
3 5 1 0.535145 0.535145
4 5 1 0.514343 0.514343
5 5 1 0.5 0.5
TEST067
For the F PDF:
F_CDF evaluates the CDF;
F_PDF evaluates the PDF;
F_SAMPLE samples the PDF;
PDF parameter M = 1
PDF parameter N = 1
X PDF CDF
8.79828 0.0109522 0.792993
0.913042 0.174133 0.485526
0.552007 0.276048 0.406792
0.00347467 5.38129 0.037483
0.0161641 2.46383 0.0805067
0.0212137 2.14006 0.0920758
1.26646 0.124798 0.537509
0.00713115 3.74269 0.0536328
2.23222 0.0659146 0.624499
0.060063 1.22522 0.153005
TEST068
For the F PDF:
F_MEAN computes the mean;
F_SAMPLE samples;
F_VARIANCE computes the variance;
PDF parameter M = 8
PDF parameter N = 6
PDF mean = 1.5
PDF variance = 3.375
Sample size = 1000
Sample mean = 1.65874
Sample variance = 29.2135
Sample maximum = 164.816
Sample minimum = 0.0826478
TEST069
FACTORIAL_LOG evaluates the log of the factorial function;
GAMMA_LOG_INT evaluates the log for integer argument.
I, GAMMA_LOG_INT(I+1) FACTORIAL_LOG(I)
1 0 0
2 0.693147 0.693147
3 1.79176 1.79176
4 3.17805 3.17805
5 4.78749 4.78749
6 6.57925 6.57925
7 8.52516 8.52516
8 10.6046 10.6046
9 12.8018 12.8018
10 15.1044 15.1044
11 17.5023 17.5023
12 19.9872 19.9872
13 22.5522 22.5522
14 25.1912 25.1912
15 27.8993 27.8993
16 30.6719 30.6719
17 33.5051 33.5051
18 36.3954 36.3954
19 39.3399 39.3399
20 42.3356 42.3356
TEST070
FACTORIAL_STIRLING computes Stirling's
approximate factorial function;
I4_FACTORIAL evaluates the factorial function;
N Stirling N!
0 1 1
1 1.00227 1
2 2.00065 2
3 6.0006 6
4 24.001 24
5 120.003 120
6 720.009 720
7 5040.04 5040
8 40320.2 40320
9 362881 362880
10 3.62881e+06 3.6288e+06
11 3.99169e+07 3.99168e+07
12 4.79002e+08 4.79002e+08
13 6.22703e+09 6.22702e+09
14 8.71784e+10 8.71783e+10
15 1.30768e+12 1.30767e+12
16 2.09228e+13 2.09228e+13
17 3.55688e+14 3.55687e+14
18 6.40238e+15 6.40237e+15
19 1.21645e+17 1.21645e+17
20 2.4329e+18 2.4329e+18
TEST0705
For the Fisher PDF:
FISHER_PDF evaluates the PDF.
FISHER_SAMPLE samples the PDF.
PDF parameters:
Concentration parameter KAPPA = 0
Direction MU(1:3) = 1 0 0
X PDF
-0.563163 0.312518 -0.76497 0.0795775
0.912635 0.127444 0.388401 0.0795775
0.659018 0.43708 0.612091 0.0795775
0.123391 -0.99193 -0.0291358 0.0795775
-0.169386 -0.942369 -0.28853 0.0795775
-0.867763 0.00574039 -0.496946 0.0795775
-0.484844 -0.52511 -0.699418 0.0795775
-0.780086 0.504435 0.370149 0.0795775
-0.912342 0.229164 -0.339288 0.0795775
0.267931 0.0823288 -0.959914 0.0795775
PDF parameters:
Concentration parameter KAPPA = 0.5
Direction MU(1:3) = 1 0 0
X PDF
-0.36265 0.352448 -0.862708 0.0636934
0.943998 0.102869 0.313505 0.122414
0.771936 0.369422 0.517342 0.112322
0.351138 -0.93592 -0.0274906 0.0910105
0.0772099 -0.953331 -0.291887 0.0793613
-0.784785 0.00715868 -0.619727 0.0515738
-0.267118 -0.578584 -0.770642 0.0668096
-0.653881 0.609991 0.447605 0.0550623
-0.854781 0.290486 -0.430078 0.0498
0.473689 0.0752579 -0.877471 0.0967616
PDF parameters:
Concentration parameter KAPPA = 10
Direction MU(1:3) = 1 0 0
X PDF
0.847866 0.200522 -0.490831 0.347624
0.995533 0.029434 0.0897036 1.52203
0.981308 0.111834 0.156614 1.3202
0.94232 -0.334568 -0.0098272 0.893966
0.912126 -0.391949 -0.120005 0.660982
0.72837 0.00791427 -0.685139 0.105231
0.864357 -0.301929 -0.402153 0.409948
0.779233 0.505291 0.370778 0.175002
0.687254 0.406587 -0.601971 0.069756
0.954424 0.0255038 -0.297363 1.00899
TEST071
For the Fisk PDF:
FISK_CDF evaluates the CDF;
FISK_CDF_INV inverts the CDF.
FISK_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF CDF_INV
2.30758 0.391667 0.218418 2.30758
6.59494 0.0223993 0.956318 6.59494
4.38899 0.125191 0.829509 4.38899
3.17239 0.339985 0.561695 3.17239
2.78448 0.408233 0.415307 2.78448
1.82738 0.223887 0.0661187 1.82738
2.40534 0.408224 0.257578 2.40534
1.99609 0.29475 0.109957 1.99609
1.71577 0.175649 0.043829 1.71577
3.40184 0.289844 0.633966 3.40184
TEST072
For the Fisk PDF:
FISK_MEAN computes the mean;
FISK_SAMPLE samples;
FISK_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 3.4184
PDF variance = 3.82494
Sample size = 1000
Sample mean = 3.4112
Sample variance = 2.91484
Sample maximum = 16.6277
Sample minimum = 1.24516
TEST073
For the Folded Normal PDF:
FOLDED_NORMAL_CDF evaluates the CDF;
FOLDED_NORMAL_CDF_INV inverts the CDF.
FOLDED_NORMAL_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
1.03703 0.205965 0.218421 1.03703
7.16445 0.0314698 0.956292 7.16364
4.97681 0.0901798 0.829447 4.97609
2.86891 0.163148 0.561656 2.86863
2.03443 0.186808 0.415234 2.03394
0.310759 0.212331 0.0661153 0.310758
1.22833 0.203183 0.257565 1.22824
0.517615 0.211208 0.109931 0.517593
0.206128 0.212686 0.043879 0.206146
3.33313 0.147866 0.633889 3.33255
TEST074
For the Folded Normal PDF:
FOLDED_NORMAL_MEAN computes the mean;
FOLDED_NORMAL_SAMPLE samples;
FOLDED_NORMAL_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 2.90672
PDF variance = 4.55099
Sample size = 1000
Sample mean = 2.92096
Sample variance = 4.50179
Sample maximum = 10.6319
Sample minimum = 0.00881944
TEST0744
For the Frechet PDF:
FRECHET_CDF evaluates the CDF;
FRECHET_CDF_INV inverts the CDF.
FRECHET_PDF evaluates the PDF;
PDF parameter ALPHA = 3
X PDF CDF CDF_INV
0.869476 1.14652 0.218418 0.869476
2.81845 0.0454656 0.956318 2.81845
1.74896 0.265962 0.829509 1.74896
1.20132 0.809067 0.561695 1.20132
1.04403 1.04866 0.415307 1.04403
0.716705 0.751767 0.0661187 0.716705
0.903373 1.16028 0.257578 0.903373
0.76799 0.948247 0.109957 0.76799
0.683811 0.601365 0.043829 0.683811
1.29943 0.667067 0.633966 1.29943
TEST0745
For the Frechet PDF:
FRECHET_MEAN computes the mean;
FRECHET_SAMPLE samples;
FRECHET_VARIANCE computes the variance;
PDF parameter ALPHA = 3
PDF mean = 1.35412
PDF variance = 0.845303
Sample size = 1000
Sample mean = 1.35005
Sample variance = 0.61922
Sample maximum = 7.81659
Sample minimum = 0.541476
TEST075
TGAMMA evaluates the Gamma function;
GAMMA_LOG evaluates the log of the Gamma function;
GAMMA_LOG_INT evaluates the log for integer argument;
I4_FACTORIAL evaluates the factorial function.
X, TGAMMA(X), Exp(GAMMA_LOG(X)), Exp(GAMMA_LOG_INT(X)) I4_FACTORIAL(X+1)
1 1 1 1 1
2 1 1 1 1
3 2 2 2 2
4 6 6 6 6
5 24 24 24 24
6 120 120 120 120
7 720 720 720 720
8 5040 5040 5040 5040
9 40320 40320 40320 40320
10 362880 362880 362880 362880
TEST076:
GAMMA_INC evaluates the normalized incomplete Gamma
function GAMMA_INC(A,B,X).
GAMMA_INC_VALUES returns some exact values.
A X Exact F GAMMA_INC(A,X)
0.1 0.03 2.4903 0.738235
0.1 0.3 0.871837 0.908358
0.1 1.5 0.107921 0.988656
0.5 0.075 1.23812 0.301465
0.5 0.75 0.39113 0.779329
0.5 3.5 0.0144472 0.991849
1 0.1 0.904837 0.0951626
1 1 0.367879 0.632121
1 5 0.00673795 0.993262
1.1 0.1 0.882797 0.0720597
1.1 1 0.390833 0.589181
1.1 5 0.00805146 0.991537
2 0.15 0.989814 0.0101858
2 1.5 0.557825 0.442175
2 7 0.00729506 0.992705
6 2.5 114.957 0.042021
6 12 2.44092 0.979659
11 16 280855 0.922604
26 25 8.57648e+24 0.447079
41 45 2.08503e+47 0.744455
TEST077
For the Gamma PDF:
GAMMA_CDF evaluates the CDF;
GAMMA_PDF evaluates the PDF;
GAMMA_SAMPLE samples the PDF;
PDF parameter A = 1
PDF parameter B = 1.5
PDF parameter B = 3
X PDF CDF
9.78938 0.0326457 0.931465
3.52763 0.175509 0.238845
4.49151 0.176127 0.411287
7.07259 0.0953344 0.768902
5.28905 0.156175 0.544577
14.503 0.0033268 0.993778
8.13457 0.0648279 0.853273
10.4424 0.024378 0.94997
5.8157 0.138588 0.622277
4.28548 0.178916 0.37469
TEST078
For the Gamma PDF:
GAMMA_MEAN computes the mean;
GAMMA_SAMPLE samples;
GAMMA_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 3
PDF parameter C = 2
PDF mean = 7
PDF variance = 18
Sample size = 1000
Sample mean = 7.13589
Sample variance = 18.7835
Sample maximum = 32.6521
Sample minimum = 1.12016
TEST079
For the Genlogistic PDF:
GENLOGISTIC_CDF evaluates the CDF;
GENLOGISTIC_CDF_INV inverts the CDF.
GENLOGISTIC_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF CDF_INV
1.82954 0.13032 0.218418 1.82954
9.39944 0.0211989 0.956318 9.39944
6.48873 0.0751605 0.829509 6.48873
4.10241 0.147371 0.561695 4.10241
3.15571 0.158177 0.415307 3.15571
0.22539 0.0590738 0.0661187 0.22539
2.11836 0.140536 0.257578 2.11836
0.832536 0.0859182 0.109957 0.832536
-0.215463 0.0425639 0.043829 -0.215463
4.61496 0.13403 0.633966 4.61496
TEST080
For the Genlogistic PDF:
GENLOGISTIC_MEAN computes the mean;
GENLOGISTIC_SAMPLE samples;
GENLOGISTIC_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 4
PDF variance = 8.15947
Sample size = 1000
Sample mean = 4.00819
Sample variance = 8.13473
Sample maximum = 15.534
Sample minimum = -2.93789
TEST081
For the Geometric PDF:
GEOMETRIC_CDF evaluates the CDF;
GEOMETRIC_CDF_INV inverts the CDF.
GEOMETRIC_PDF evaluates the PDF;
PDF parameter A = 0.25
X PDF CDF CDF_INV
1 0.25 0.25 2
11 0.0140784 0.957765 12
7 0.0444946 0.866516 8
3 0.140625 0.578125 4
2 0.1875 0.4375 3
1 0.25 0.25 2
2 0.1875 0.4375 3
1 0.25 0.25 2
1 0.25 0.25 2
4 0.105469 0.683594 5
TEST082
For the Geometric PDF:
GEOMETRIC_MEAN computes the mean;
GEOMETRIC_SAMPLE samples;
GEOMETRIC_VARIANCE computes the variance.
PDF parameter A = 0.25
PDF mean = 4
PDF variance = 12
Sample size = 1000
Sample mean = 4.022
Sample variance = 11.7413
Sample maximum = 22
Sample minimum = 1
TEST083
For the Geometric PDF:
GEOMETRIC_CDF evaluates the CDF;
GEOMETRIC_PDF evaluates the PDF;
PDF parameter A = 0.25
X PDF CDF
0 0 0
1 0.25 0.25
2 0.1875 0.4375
3 0.140625 0.578125
4 0.105469 0.683594
5 0.0791016 0.762695
6 0.0593262 0.822021
7 0.0444946 0.866516
8 0.033371 0.899887
9 0.0250282 0.924915
10 0.0187712 0.943686
TEST084
For the Gompertz PDF:
GOMPERTZ_CDF evaluates the CDF;
GOMPERTZ_CDF_INV inverts the CDF.
GOMPERTZ_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
0.0798917 2.47825 0.218418 0.0798917
0.785233 0.225843 0.956318 0.785233
0.494408 0.720533 0.829509 0.494408
0.251663 1.56551 0.561695 0.251663
0.168638 1.97158 0.415307 0.168638
0.0226237 2.84592 0.0661187 0.0226237
0.0960122 2.38054 0.257578 0.0960122
0.0383151 2.74199 0.109957 0.0383151
0.0148627 2.89822 0.043829 0.0148627
0.301249 1.35309 0.633966 0.301249
TEST085
For the Gompertz PDF:
GOMPERTZ_MEAN computes the mean;
GOMPERTZ_SAMPLE samples;
GOMPERTZ_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
Sample size = 1000
Sample mean = 0.279586
Sample variance = 0.0569063
Sample maximum = 1.2783
Sample minimum = 0.000613224
TEST086
For the Gumbel PDF:
GUMBEL_CDF evaluates the CDF;
GUMBEL_CDF_INV inverts the CDF.
GUMBEL_PDF evaluates the PDF;
X PDF CDF CDF_INV
-0.419594 0.332289 0.218418 -0.419594
3.10856 0.0427141 0.956318 3.10856
1.67707 0.155053 0.829509 1.67707
0.550268 0.323983 0.561695 0.550268
0.12927 0.364946 0.415307 0.12927
-0.999272 0.179599 0.0661187 -0.999272
-0.304859 0.349387 0.257578 -0.304859
-0.791937 0.242748 0.109957 -0.791937
-1.14022 0.137073 0.043829 -1.14022
0.785788 0.288936 0.633966 0.785788
TEST087
For the Gumbel PDF:
GUMBEL_MEAN computes the mean;
GUMBEL_SAMPLE samples;
GUMBEL_VARIANCE computes the variance.
PDF mean = 0.577216
PDF variance = 1.64493
Sample size = 1000
Sample mean = 0.581659
Sample variance = 1.63026
Sample maximum = 6.16874
Sample minimum = -1.84037
TEST088
For the Half Normal PDF:
HALF_NORMAL_CDF evaluates the CDF;
HALF_NORMAL_CDF_INV inverts the CDF.
HALF_NORMAL_PDF evaluates the PDF;
PDF parameter A = 0
PDF parameter B = 2
X PDF CDF CDF_INV
0.554517 0.383899 0.218418 0.554517
4.03425 0.0521654 0.956318 4.03425
2.74126 0.155945 0.829509 2.74126
1.55012 0.295438 0.561695 1.55012
1.09309 0.343595 0.415307 1.09309
0.165925 0.397572 0.0661187 0.165925
0.657295 0.377969 0.257578 0.657295
0.276499 0.395148 0.109957 0.276499
0.109918 0.39834 0.043829 0.109918
1.80785 0.265145 0.633966 1.80785
TEST089
For the Half Normal PDF:
HALF_NORMAL_MEAN computes the mean;
HALF_NORMAL_SAMPLE samples;
HALF_NORMAL_VARIANCE computes the variance;
PDF parameter A = 0
PDF parameter B = 10
PDF mean = 7.97885
PDF variance = 36.338
Sample size = 1000
Sample mean = 8.01612
Sample variance = 35.9155
Sample maximum = 30.769
Sample minimum = 0.0230406
TEST090
For the Hypergeometric PDF:
HYPERGEOMETRIC_CDF evaluates the CDF.
HYPERGEOMETRIC_PDF evaluates the PDF.
Total number of balls L = 1000
Number of white balls M = 70
Number of balls taken N = 100
PDF argument X = 7
PDF value = = 0.162835
CDF value = = 0.599487
TEST091
For the Hypergeometric PDF:
HYPERGEOMETRIC_MEAN computes the mean;
HYPERGEOMETRIC_SAMPLE samples;
HYPERGEOMETRIC_VARIANCE computes the variance.
Total number of balls L = 1000
Number of white balls M = 70
Number of balls taken N = 100
PDF mean = 7
PDF variance = 1.5656
THIS CALL IS TAKING FOREVER!
TEST092
R8_CEILING rounds an R8 up.
X R8_CEILING(X)
-1.2 -1
-1 -1
-0.8 0
-0.6 0
-0.4 0
-0.2 0
0 0
0.2 1
0.4 1
0.6 1
0.8 1
1 1
1.2 2
TEST093
For the Inverse Gaussian PDF:
INVERSE_GAUSSIAN_CDF evaluates the CDF;
INVERSE_GAUSSIAN_PDF evaluates the PDF;
PDF parameter A = 5
PDF parameter B = 2
X PDF CDF
0.559532 0.329239 0.0861168
1.28731 0.251704 0.307572
0.853592 0.319635 0.18353
1.35825 0.241176 0.325052
5.32365 0.0458954 0.744699
0.226285 0.0933236 0.00436661
0.366732 0.244354 0.0287975
2.59887 0.123228 0.539812
0.741461 0.332202 0.146927
1.89165 0.176781 0.435385
TEST094
For the Inverse Gaussian PDF:
INVERSE_GAUSSIAN_MEAN computes the mean;
INVERSE_GAUSSIAN_SAMPLE samples;
INVERSE_GAUSSIAN_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 2
PDF variance = 2.66667
Sample size = 1000
Sample mean = 1.95731
Sample variance = 2.26428
Sample maximum = 12.1368
Sample minimum = 0.215551
TEST095
For the Laplace PDF:
LAPLACE_CDF evaluates the CDF;
LAPLACE_CDF_INV inverts the CDF.
LAPLACE_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
X PDF CDF CDF_INV
-0.656392 0.109209 0.218418 -0.656392
5.87532 0.0218412 0.956318 5.87532
3.15185 0.0852454 0.829509 3.15185
1.26339 0.219152 0.561695 1.26339
0.62882 0.207654 0.415307 0.62882
-3.04631 0.0330594 0.0661187 -3.04631
-0.326573 0.128789 0.257578 -0.326573
-2.02904 0.0549784 0.109957 -2.02904
-3.86862 0.0219145 0.043829 -3.86862
1.62376 0.183017 0.633966 1.62376
TEST096
For the Laplace PDF:
LAPLACE_MEAN computes the mean;
LAPLACE_SAMPLE samples;
LAPLACE_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF mean = 1
PDF variance = 8
Sample size = 1000
Sample mean = 0.994018
Sample variance = 8.10829
Sample maximum = 11.9533
Sample minimum = -10.2115
TEST0965
For the Levy PDF:
LEVY_CDF evaluates the CDF;
LEVY_CDF_INV inverts the CDF.
LEVY_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
X PDF CDF CDF_INV
2.32036 0.174367 0.218418 2.32036
667.596 3.27326e-05 0.956318 667.596
44.1337 0.00194595 0.829509 44.1337
6.93865 0.032943 0.561695 6.93865
4.01406 0.0773762 0.415307 4.01406
1.59227 0.228757 0.0661187 1.59227
2.56039 0.152493 0.257578 2.56039
1.78283 0.227065 0.109957 1.78283
1.49223 0.214227 0.043829 1.49223
9.82141 0.0192259 0.633966 9.82141
TEST097
For the Logistic PDF:
LOGISTIC_CDF evaluates the CDF;
LOGISTIC_CDF_INV inverts the CDF.
LOGISTIC_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
X PDF CDF CDF_INV
-1.54982 0.0853559 0.218418 -1.54982
7.17229 0.0208871 0.956318 7.17229
4.16431 0.0707118 0.829509 4.16431
1.49609 0.123097 0.561695 1.49609
0.315863 0.121414 0.415307 0.315863
-4.29579 0.0308735 0.0661187 -4.29579
-1.11719 0.0956157 0.257578 -1.11719
-3.18237 0.0489331 0.109957 -3.18237
-5.16528 0.020954 0.043829 -5.16528
2.09854 0.116027 0.633966 2.09854
TEST098
For the Logistic PDF:
LOGISTIC_MEAN computes the mean;
LOGISTIC_SAMPLE samples;
LOGISTIC_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 2
PDF variance = 29.6088
Sample size = 1000
Sample mean = 2.00703
Sample variance = 29.8759
Sample maximum = 20.5031
Sample minimum = -16.8911
TEST099
For the Log Normal PDF:
LOG_NORMAL_CDF evaluates the CDF;
LOG_NORMAL_CDF_INV inverts the CDF.
LOG_NORMAL_PDF evaluates the PDF;
PDF parameter A = 10
PDF parameter B = 2.25
X PDF CDF CDF_INV
3829.62 3.42207e-05 0.218418 3829.62
1.03126e+06 3.98836e-08 0.956318 1.03126e+06
187683 6.00352e-07 0.829509 187683
31236.9 5.60821e-06 0.561695 31236.9
13611.8 1.27314e-05 0.415307 13611.8
744.708 7.66792e-05 0.0661187 744.708
5093.04 2.8169e-05 0.257578 5093.04
1393.81 5.99421e-05 0.109957 1393.81
472.134 8.73521e-05 0.043829 472.134
47588.4 3.51376e-06 0.633966 47588.4
TEST100
For the LogNormal PDF:
LOG_NORMAL_MEAN computes the mean;
LOG_NORMAL_SAMPLE samples;
LOG_NORMAL_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF mean = 20.0855
PDF variance = 21623
Sample size = 1000
Sample mean = 18.2209
Sample variance = 3776.12
Sample maximum = 835.466
Sample minimum = 0.00815371
TEST101
For the Log Series PDF:
LOG_SERIES_CDF evaluates the CDF;
LOG_SERIES_CDF_INV inverts the CDF.
LOG_SERIES_PDF evaluates the PDF;
PDF parameter A = 0.25
X PDF CDF CDF_INV
1 0.869015 0.869015 2
1 0.869015 0.869015 2
2 0.108627 0.977642 3
1 0.869015 0.869015 2
1 0.869015 0.869015 2
1 0.869015 0.869015 2
1 0.869015 0.869015 2
4 0.00339459 0.999141 5
1 0.869015 0.869015 2
2 0.108627 0.977642 3
TEST102
For the Log Series PDF:
LOG_SERIES_CDF evaluates the CDF;
LOG_SERIES_PDF evaluates the PDF;
PDF parameter A = 0.25
X PDF CDF
1 0.869015 0.869015
2 0.108627 0.977642
3 0.0181045 0.995746
4 0.00339459 0.999141
5 0.000678918 0.99982
6 0.000141441 0.999961
7 3.03088e-05 0.999991
8 6.63006e-06 0.999998
9 1.47335e-06 1
10 3.31503e-07 1
TEST103
For the Log Series PDF:
LOG_SERIES_MEAN computes the mean;
LOG_SERIES_SAMPLE samples;
LOG_SERIES_VARIANCE computes the variance.
PDF parameter A = 0.25
PDF mean = 1.15869
PDF variance = 0.202361
Sample size = 1000
Sample mean = 1.165
Sample variance = 0.213989
Sample maximum = 4
Sample minimum = 1
TEST104
For the Log Uniform PDF:
LOG_UNIFORM_CDF evaluates the CDF;
LOG_UNIFORM_CDF_INV inverts the CDF.
LOG_UNIFORM_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 20
X PDF CDF CDF_INV
3.30711 0.131322 0.218418 3.30711
18.0862 0.0240125 0.956318 18.0862
13.5064 0.0321547 0.829509 13.5064
7.28996 0.0595743 0.561695 7.28996
5.204 0.083454 0.415307 5.204
2.32889 0.186481 0.0661187 2.32889
3.61916 0.119999 0.257578 3.61916
2.57624 0.168577 0.109957 2.57624
2.21238 0.196302 0.043829 2.21238
8.60985 0.0504416 0.633966 8.60985
TEST105
For the Log Uniform PDF:
LOG_UNIFORM_MEAN computes the mean;
LOG_UNIFORM_SAMPLE samples;
PDF parameter A = 2
PDF parameter B = 20
PDF mean = 7.8173
Sample size = 1000
Sample mean = 7.8421
Sample variance = 24.5202
Sample maximum = 19.9039
Sample minimum = 2.00848
TEST106
For the Lorentz PDF:
LORENTZ_CDF evaluates the CDF;
LORENTZ_CDF_INV inverts the CDF.
LORENTZ_PDF evaluates the PDF;
X PDF CDF CDF_INV
-1.2211 0.12778 0.218418 -1.2211
7.24111 0.00595711 0.956318 7.24111
1.68497 0.0829119 0.829509 1.68497
0.196286 0.306501 0.561695 0.196286
-0.272532 0.296302 0.415307 -0.272532
-4.74478 0.0135377 0.0661187 -4.74478
-0.953486 0.16673 0.257578 -0.953486
-2.77879 0.0364964 0.109957 -2.77879
-7.21659 0.0059969 0.043829 -7.21659
0.447611 0.26518 0.633966 0.447611
TEST107
For the Lorentz PDF:
LORENTZ_MEAN computes the mean;
LORENTZ_SAMPLE samples;
LORENTZ_VARIANCE computes the variance.
PDF mean = 0
PDF variance = inf
Sample size = 1000
Sample mean = -0.111859
Sample variance = 175.49
Sample maximum = 152.177
Sample minimum = -173.146
TEST108
For the Maxwell PDF:
MAXWELL_CDF evaluates the CDF;
MAXWELL_CDF_INV inverts the CDF.
MAXWELL_PDF evaluates the PDF;
PDF parameter A = 2
X PDF CDF CDF_INV
4.29456 0.183427 0.768636 4.29492
6.13704 0.0338961 0.89487 6.13672
1.45642 0.162283 0.307636 1.45605
5.98388 0.040642 0.887603 5.98438
3.74497 0.242317 0.709648 3.74414
2.0281 0.245322 0.433405 2.02832
1.7946 0.214758 0.383889 1.79492
1.95034 0.235816 0.417222 1.9502
1.49461 0.168514 0.316485 1.49463
1.35125 0.144944 0.282999 1.35156
TEST109
For the Maxwell PDF:
MAXWELL_MEAN computes the mean;
MAXWELL_SAMPLE samples;
MAXWELL_VARIANCE computes the variance.
PDF parameter A = 2
PDF mean = 3.19154
PDF variance = 1.81408
Sample size = 1000
Sample mean = 3.15337
Sample variance = 1.9332
Sample maximum = 8.32689
Sample minimum = 0.206015
TEST110
MULTINOMIAL_COEF1 computes multinomial
coefficients using the Gamma function;
MULTINOMIAL_COEF2 computes multinomial
coefficients directly.
Line 10 of the BINOMIAL table:
0 10 1 1
1 9 10 10
2 8 45 45
3 7 120 120
4 6 210 210
5 5 252 252
6 4 210 210
7 3 120 120
8 2 45 45
9 1 10 10
10 0 1 1
Level 5 of the TRINOMIAL coefficients:
0 0 5 1 1
0 1 4 5 5
0 2 3 10 10
0 3 2 10 10
0 4 1 5 5
0 5 0 1 1
1 0 4 5 5
1 1 3 20 20
1 2 2 30 30
1 3 1 20 20
1 4 0 5 5
2 0 3 10 10
2 1 2 30 30
2 2 1 30 30
2 3 0 10 10
3 0 2 10 10
3 1 1 20 20
3 2 0 10 10
4 0 1 5 5
4 1 0 5 5
5 0 0 1 1
TEST111
For the Multinomial PDF:
MULTINOMIAL_MEAN computes the mean;
MULTINOMIAL_SAMPLE samples;
MULTINOMIAL_VARIANCE computes the variance;
PDF parameter A = 5
PDF parameter B = 3
PDF parameter C:
1 0.125
2 0.5
3 0.375
PDF mean:
1 0.625
2 2.5
3 1.875
PDF variance:
1 0.546875
2 1.25
3 1.17188
Sample size = 1000
Component Mean, Variance, Min, Max:
1 0.628 0.552168 0 3
2 2.472 1.23445 0 5
3 1.9 1.20721 0 5
TEST112
For the Multinomial PDF:
MULTINOMIAL_PDF evaluates the PDF;
PDF parameter A = 5
PDF parameter B = 3
PDF parameter C:
1 0.1
2 0.5
3 0.4
PDF argument X:
0 0
1 2
2 3
PDF value = 0.16
TEST113
For the Nakagami PDF:
NAKAGAMI_CDF evaluates the CDF;
NAKAGAMI_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
X PDF CDF
1.25 0.000393121 1.65738e-05
TEST114
For the Nakagami PDF:
NAKAGAMI_MEAN evaluates the mean;
NAKAGAMI_VARIANCE evaluates the variance;
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF mean = 2.91874
PDF variance = 0.318446
TEST1145
For the Negative Binomial PDF:
NEGATIVE_BINOMIAL_CDF evaluates the CDF;
NEGATIVE_BINOMIAL_CDF_INV inverts the CDF.
NEGATIVE_BINOMIAL_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 0.25
X PDF CDF CDF_INV
6 0.098877 0.466064 6
3 0.09375 0.15625 3
7 0.0889893 0.555054 7
4 0.105469 0.261719 4
4 0.105469 0.261719 4
13 0.0316764 0.873295 13
8 0.0778656 0.632919 8
6 0.098877 0.466064 6
12 0.0387155 0.841618 12
6 0.098877 0.466064 6
TEST1146
For the Negative Binomial PDF:
NEGATIVE_BINOMIAL_MEAN computes the mean;
NEGATIVE_BINOMIAL_SAMPLE samples;
NEGATIVE_BINOMIAL_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 0.75
PDF mean = 2.66667
PDF variance = 0.888889
Sample size = 1000
Sample mean = 2.688
Sample variance = 0.833489
Sample maximum = 8
Sample minimum = 2
TEST115
For the Normal 01 PDF:
NORMAL_01_CDF evaluates the CDF;
NORMAL_01_CDF_INV inverts the CDF.
NORMAL_01_PDF evaluates the PDF;
X PDF CDF CDF_INV
1.679040256736491 0.0974392 0.953428 1.679040256746338
-0.5660598123302577 0.339884 0.285677 -0.5660598123353983
1.21293421737931 0.191179 0.887423 1.212934217394378
1.269380628984426 0.178244 0.897847 1.269380629005457
-1.666086672831968 0.0995733 0.0478481 -1.666086672843646
-2.242464038261558 0.0322815 0.0124657 -2.242464038262084
0.0396749185148341 0.398628 0.515824 0.03967491851894145
0.6730681958483083 0.318081 0.749548 0.6730681958595057
-0.2751273507132183 0.384125 0.391609 -0.2751273507160336
2.164004788036971 0.0383732 0.984768 2.164004788031278
TEST116
For the Normal 01 PDF:
NORMAL_01_MEAN computes the mean;
NORMAL_01_SAMPLE samples;
NORMAL_01_VARIANCE computes the variance;
PDF mean = 0
PDF variance = 1
Sample size = 1000
Sample mean = 0.00581875
Sample variance = 0.998375
Sample maximum = 3.32858
Sample minimum = -3.02975
TEST117
For the Normal PDF:
NORMAL_CDF evaluates the CDF;
NORMAL_CDF_INV inverts the CDF.
NORMAL_PDF evaluates the PDF;
PDF parameter A = 100
PDF parameter B = 15
X PDF CDF CDF_INV
125.186 0.00649595 0.953428 125.186
91.5091 0.0226589 0.285677 91.5091
118.194 0.0127453 0.887423 118.194
119.041 0.0118829 0.897847 119.041
75.0087 0.00663822 0.0478481 75.0087
66.363 0.0021521 0.0124657 66.363
100.595 0.0265752 0.515824 100.595
110.096 0.0212054 0.749548 110.096
95.8731 0.0256084 0.391609 95.8731
132.46 0.00255821 0.984768 132.46
TEST118
For the Normal PDF:
NORMAL_MEAN computes the mean;
NORMAL_SAMPLE samples;
NORMAL_VARIANCE computes the variance;
PDF parameter A = 100
PDF parameter B = 15
PDF mean = 100
PDF variance = 225
Sample size = 1000
Sample mean = 100.087
Sample variance = 224.634
Sample maximum = 149.929
Sample minimum = 54.5537
TEST1184
For the Truncated Normal PDF:
NORMAL_TRUNCATED_AB_CDF evaluates the CDF.
NORMAL_TRUNCATED_AB_CDF_INV inverts the CDF.
NORMAL_TRUNCATED_AB_PDF evaluates the PDF.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [50,150]
X PDF CDF CDF_INV
81.63 0.0127629 0.218418 81.63
137.962 0.00527826 0.956318 137.962
122.367 0.0112043 0.829509 122.367
103.704 0.0165359 0.561695 103.704
94.899 0.016374 0.415307 94.899
65.8326 0.00657044 0.0661187 65.8326
84.5743 0.0138204 0.257578 84.5743
71.5672 0.00875626 0.109957 71.5672
62.0654 0.00528716 0.043829 62.0654
108.155 0.0158521 0.633966 108.155
TEST1185
For the Truncated Normal PDF:
NORMAL_TRUNCATED_AB_MEAN computes the mean;
NORMAL_TRUNCATED_AB_SAMPLE samples;
NORMAL_TRUNCATED_AB_VARIANCE computes the variance.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [50,150]
PDF mean = 100
PDF variance = 483.588
Sample size = 1000
Sample mean = 100.123
Sample variance = 486.064
Sample maximum = 149.108
Sample minimum = 50.7873
TEST1186
For the Lower Truncated Normal PDF:
NORMAL_TRUNCATED_A_CDF evaluates the CDF.
NORMAL_TRUNCATED_A_CDF_INV inverts the CDF.
NORMAL_TRUNCATED_A_PDF evaluates the PDF.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [50,+oo]
X PDF CDF CDF_INV
82.0355 0.0126136 0.218418 82.0355
143.008 0.00371817 0.956318 143.008
124.191 0.0102245 0.829509 124.191
104.515 0.016065 0.561695 104.515
95.5021 0.016067 0.415307 95.5021
66.0709 0.00650134 0.0661187 66.0709
85.0161 0.0136446 0.257578 85.0161
71.8645 0.00866826 0.109957 71.8645
62.2618 0.00522585 0.043829 62.2618
109.115 0.0152792 0.633966 109.115
TEST1187
For the Lower Truncated Normal PDF:
NORMAL_TRUNCATED_A_MEAN computes the mean;
NORMAL_TRUNCATED_A_SAMPLE samples;
NORMAL_TRUNCATED_A_VARIANCE computes the variance.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [50,+oo]
PDF mean = 101.381
PDF variance = 554.032
Sample size = 1000
Sample mean = 101.504
Sample variance = 555.665
Sample maximum = 171.782
Sample minimum = 50.8055
TEST1188
For the Upper Truncated Normal PDF:
NORMAL_TRUNCATED_B_CDF evaluates the CDF.
NORMAL_TRUNCATED_B_CDF_INV inverts the CDF.
NORMAL_TRUNCATED_B_PDF evaluates the PDF.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [-oo,150]
X PDF CDF CDF_INV
80.1372 0.0119094 0.218418 80.1372
137.766 0.00521699 0.956318 137.766
122.006 0.0110844 0.829509 122.006
103.073 0.0162063 0.561695 103.073
94.0447 0.0158724 0.415307 94.0447
62.0713 0.00516592 0.0661187 62.0713
83.2727 0.0130542 0.257578 83.2727
68.9956 0.00756806 0.109957 68.9956
57.0318 0.00372825 0.043829 57.0318
107.607 0.0155905 0.633966 107.607
TEST1189
For the Upper Truncated Normal PDF:
NORMAL_TRUNCATED_B_MEAN computes the mean;
NORMAL_TRUNCATED_B_SAMPLE samples;
NORMAL_TRUNCATED_B_VARIANCE computes the variance.
The parent normal distribution has
mean = 100
standard deviation = 25
The parent distribution is truncated to
the interval [-oo,150]
PDF mean = 98.6188
PDF variance = 554.032
Sample size = 1000
Sample mean = 98.7101
Sample variance = 560.281
Sample maximum = 149.087
Sample minimum = 27.2041
TEST119
For the Pareto PDF:
PARETO_CDF evaluates the CDF;
PARETO_CDF_INV inverts the CDF.
PARETO_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
2.17123 1.07992 0.218418 2.17123
5.67886 0.0230763 0.956318 5.67886
3.60686 0.141805 0.829509 3.60686
2.63292 0.499412 0.561695 2.63292
2.39178 0.733379 0.415307 2.39178
2.04613 1.36924 0.0661187 2.04613
2.20875 1.00838 0.257578 2.20875
2.07918 1.28422 0.109957 2.07918
2.0301 1.41299 0.043829 2.0301
2.79591 0.392754 0.633966 2.79591
TEST120
For the Pareto PDF:
PARETO_MEAN computes the mean;
PARETO_SAMPLE samples;
PARETO_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 3
PDF variance = 3
Sample size = 1000
Sample mean = 2.99105
Sample variance = 2.10266
Sample maximum = 15.6386
Sample minimum = 2.00123
TEST123
For the Pearson 05 PDF:
PEARSON_05_PDF evaluates the PDF.
PDF parameter A = 1
PDF parameter B = 2
PDF parameter C = 3
PDF argument X = 5
PDF value = 0.0758163
TEST124
For the Planck PDF:
PLANCK_PDF evaluates the PDF.
PLANCK_SAMPLE samples the PDF.
PDF parameter A = 2
PDF parameter B = 3
X PDF
3.673 0.0788188
3.0685 0.154193
2.78714 0.203171
5.41214 0.00777678
3.91626 0.0587186
0.782927 0.312254
1.68781 0.41945
2.8936 0.183616
1.24248 0.429598
1.20762 0.42572
TEST125
For the Planck PDF:
PLANCK_MEAN computes the mean;
PLANCK_SAMPLE samples;
PLANCK_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 3.83223
PDF variance = 0
Sample size = 1000
Sample mean = 1.93308
Sample variance = 0.99989
Sample maximum = 6.48678
Sample minimum = 0.165955
TEST126:
POISSON_CDF evaluates the cumulative distribution
function for the discrete Poisson probability
density function.
POISSON_CDF_VALUES returns some exact values.
A is the expected mean number of successes per unit time;
X is the number of successes;
POISSON_CDF is the probability of having up to X
successes in unit time.
A X Exact F POISSON_CDF(A,X)
0.02 0 0.980199 0.980199
0.1 0 0.904837 0.904837
0.1 1 0.995321 0.995321
0.5 0 0.606531 0.606531
0.5 1 0.909796 0.909796
0.5 2 0.985612 0.985612
1 0 0.367879 0.367879
1 1 0.735759 0.735759
1 2 0.919699 0.919699
1 3 0.981012 0.981012
2 0 0.135335 0.135335
2 1 0.406006 0.406006
2 2 0.676676 0.676676
2 3 0.857123 0.857123
5 0 0.00673795 0.00673795
5 1 0.0404277 0.0404277
5 2 0.124652 0.124652
5 3 0.265026 0.265026
5 4 0.440493 0.440493
5 5 0.615961 0.615961
5 6 0.762183 0.762183
TEST127
For the Poisson PDF:
POISSON_CDF evaluates the CDF;
POISSON_CDF_INV inverts the CDF.
POISSON_PDF evaluates the PDF;
PDF parameter A = 10
X PDF CDF CDF_INV
7 0.0900792 0.220221 7
16 0.0216988 0.972958 16
13 0.0729079 0.864464 13
10 0.12511 0.58304 10
9 0.12511 0.45793 9
5 0.0378333 0.067086 5
8 0.112599 0.33282 8
6 0.0630555 0.130141 6
5 0.0378333 0.067086 5
11 0.113736 0.696776 11
TEST128
For the Poisson PDF,
POISSON_SAMPLE samples the Poisson PDF.
POISSON_SAMPLE samples the Poisson PDF.
POISSON_SAMPLE samples the Poisson PDF.
PDF parameter A = 10
PDF mean = 10
PDF variance = 10
Sample size = 1000
Sample mean = 10.005
Sample variance = 10.005
Sample maximum = 20
Sample minimum = 2
TEST129
For the Power PDF:
POWER_CDF evaluates the CDF;
POWER_CDF_INV inverts the CDF.
POWER_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
X PDF CDF CDF_INV
1.40206 0.311568 0.218418 1.40206
2.93374 0.651943 0.956318 2.93374
2.73232 0.607183 0.829509 2.73232
2.24839 0.499642 0.561695 2.24839
1.93333 0.429629 0.415307 1.93333
0.771407 0.171424 0.0661187 0.771407
1.52256 0.338347 0.257578 1.52256
0.994792 0.221065 0.109957 0.994792
0.628061 0.139569 0.043829 0.628061
2.38866 0.530813 0.633966 2.38866
TEST130
For the Power PDF:
POWER_MEAN computes the mean;
POWER_SAMPLE samples;
POWER_VARIANCE computes the variance;
PDF parameter A = 2
PDF parameter B = 3
PDF mean = 2
PDF variance = 0.5
Sample size = 1000
Sample mean = 2.00568
Sample variance = 0.505123
Sample maximum = 2.99686
Sample minimum = 0.128629
TEST1304
For the Quasigeometric PDF:
QUASIGEOMETRIC_CDF evaluates the CDF;
QUASIGEOMETRIC_CDF_INV inverts the CDF.
QUASIGEOMETRIC_PDF evaluates the PDF;
PDF parameter A = 0.4825
PDF parameter B = 0.5893
X PDF CDF CDF_INV
0 0.4825 0.4825 1
5 0.0256319 0.963222 6
3 0.0738088 0.894094 4
1 0.212537 0.695037 2
0 0.4825 0.4825 1
0 0.4825 0.4825 1
0 0.4825 0.4825 1
0 0.4825 0.4825 1
0 0.4825 0.4825 1
1 0.212537 0.695037 2
TEST1306
For the Quasigeometric PDF:
QUASIGEOMETRIC_MEAN computes the mean;
QUASIGEOMETRIC_SAMPLE samples;
QUASIGEOMETRIC_VARIANCE computes the variance.
PDF parameter A = 0.4825
PDF parameter B = 0.5893
PDF mean = 1.26004
PDF variance = 3.28832
Sample size = 1000
Sample mean = 1.267
Sample variance = 3.21693
Sample maximum = 11
Sample minimum = 0
TEST131
For the Rayleigh PDF:
RAYLEIGH_CDF evaluates the CDF;
RAYLEIGH_CDF_INV inverts the CDF.
RAYLEIGH_PDF evaluates the PDF;
PDF parameter A = 2
X PDF CDF CDF_INV
1.4041 0.274354 0.218418 1.4041
5.00465 0.0546538 0.956318 5.00465
3.76199 0.160346 0.829509 3.76199
2.5688 0.281479 0.561695 2.5688
2.07204 0.302877 0.415307 2.07204
0.739762 0.172712 0.0661187 0.739762
1.5436 0.286501 0.257578 1.5436
0.96534 0.214799 0.109957 0.96534
0.598789 0.143136 0.043829 0.598789
2.83553 0.259475 0.633966 2.83553
TEST132
For the Rayleigh PDF:
RAYLEIGH_MEAN computes the mean;
RAYLEIGH_SAMPLE samples;
RAYLEIGH_VARIANCE computes the variance.
PDF parameter A = 2
PDF mean = 2.50663
PDF variance = 1.71681
Sample size = 1000
Sample mean = 2.5139
Sample variance = 1.70827
Sample maximum = 7.02555
Sample minimum = 0.121328
TEST133
For the Reciprocal PDF:
RECIPROCAL_CDF evaluates the CDF;
RECIPROCAL_CDF_INV inverts the CDF.
RECIPROCAL_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 3
X PDF CDF CDF_INV
1.27119 0.71605 0.218418 1.27119
2.85943 0.318329 0.956318 2.85943
2.48758 0.365914 0.829509 2.48758
1.85352 0.491087 0.561695 1.85352
1.57816 0.576771 0.415307 1.57816
1.07534 0.846465 0.0661187 1.07534
1.32708 0.685898 0.257578 1.32708
1.1284 0.806664 0.109957 1.1284
1.04933 0.867449 0.043829 1.04933
2.00668 0.453604 0.633966 2.00668
TEST134
For the Reciprocal PDF:
RECIPROCAL_MEAN computes the mean;
RECIPROCAL_SAMPLE samples;
RECIPROCAL_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 3
PDF mean = 1.82048
PDF variance = 0.326815
Sample size = 1000
Sample mean = 1.8251
Sample variance = 0.321955
Sample maximum = 2.99311
Sample minimum = 1.00202
TEST1341:
RIBESL computes values of Bessel functions
of NONINTEGER order.
BESSEL_IX_VALUES returns selected values of the
Bessel function In for NONINTEGER order.
ALPHA X FX FX2
(table) (RIBESL)
0.5 0.2 0.359208 0.359208
0.5 1 0.937675 0.937675
0.5 2 2.04624 2.04624
0.5 2.5 3.05309 3.05309
0.5 3 4.61482 4.61482
0.5 5 26.4775 26.4775
0.5 10 2778.78 2778.78
0.5 20 4.32797e+07 4.32797e+07
1.5 1 0.293525 0.293525
1.5 2 1.09947 1.09947
1.5 5 21.1844 21.1844
1.5 10 2500.91 2500.91
1.5 50 2.86665e+20 2.86665e+20
2.5 1 0.0570989 0.0570989
2.5 2 0.397027 0.397027
2.5 5 13.7669 13.7669
2.5 10 2028.51 2028.51
2.5 50 2.75316e+20 2.75316e+20
1.25 1 0.413942 0.413942
1.25 2 1.3402 1.3402
1.25 5 22.8572 22.8572
1.25 10 2593.01 2593.01
1.25 50 2.88663e+20 2.88663e+20
2.75 1 0.0359091 0.0359091
2.75 2 0.293111 0.293111
2.75 5 11.994 11.994
2.75 10 1894.58 1894.58
2.75 50 2.71691e+20 2.71691e+20
TEST1342
For the RUNS PDF:
RUNS_PDF evaluates the PDF;
M is the number of symbols of one kind,
N is the number of symbols of the other kind,
R is the number of runs (sequences of one symbol)
M N R PDF
6 0 1 1
6 0 2 0
6 1
6 1 1 0
6 1 2 0.285714
6 1 3 0.714286
6 1 4 0
6 1
6 2 1 0
6 2 2 0.0714286
6 2 3 0.214286
6 2 4 0.357143
6 2 5 0.357143
6 2 6 0
6 1
6 3 1 0
6 3 2 0.0238095
6 3 3 0.0833333
6 3 4 0.238095
6 3 5 0.297619
6 3 6 0.238095
6 3 7 0.119048
6 3 8 0
6 1
6 4 1 0
6 4 2 0.00952381
6 4 3 0.0380952
6 4 4 0.142857
6 4 5 0.214286
6 4 6 0.285714
6 4 7 0.190476
6 4 8 0.0952381
6 4 9 0.0238095
6 4 10 0
6 1
6 5 1 0
6 5 2 0.004329
6 5 3 0.0194805
6 5 4 0.0865801
6 5 5 0.151515
6 5 6 0.25974
6 5 7 0.21645
6 5 8 0.17316
6 5 9 0.0649351
6 5 10 0.021645
6 5 11 0.0021645
6 5 12 0
6 1
6 6 1 0
6 6 2 0.0021645
6 6 3 0.0108225
6 6 4 0.0541126
6 6 5 0.108225
6 6 6 0.21645
6 6 7 0.21645
6 6 8 0.21645
6 6 9 0.108225
6 6 10 0.0541126
6 6 11 0.0108225
6 6 12 0.0021645
6 6 13 0
6 6 14 0
6 1
6 7 1 0
6 7 2 0.0011655
6 7 3 0.00641026
6 7 4 0.034965
6 7 5 0.0786713
6 7 6 0.174825
6 7 7 0.203963
6 7 8 0.2331
6 7 9 0.145688
6 7 10 0.0874126
6 7 11 0.0262238
6 7 12 0.00699301
6 7 13 0.000582751
6 7 14 0
6 1
6 8 1 0
6 8 2 0.000666001
6 8 3 0.003996
6 8 4 0.02331
6 8 5 0.0582751
6 8 6 0.13986
6 8 7 0.18648
6 8 8 0.2331
6 8 9 0.174825
6 8 10 0.11655
6 8 11 0.04662
6 8 12 0.013986
6 8 13 0.002331
6 8 14 0
6 1
6 9 1 0
6 9 2 0.0003996
6 9 3 0.0025974
6 9 4 0.015984
6 9 5 0.043956
6 9 6 0.111888
6 9 7 0.167832
6 9 8 0.223776
6 9 9 0.195804
6 9 10 0.13986
6 9 11 0.0699301
6 9 12 0.0223776
6 9 13 0.00559441
6 9 14 0
6 1
TEST1344
For the RUNS PDF:
RUNS_MEAN computes the mean;
RUNS_VARIANCE computes the variance
PDF parameter M = 10
PDF parameter N = 5
PDF mean = 7.66667
PDF variance = 2.69841
Sample size = 1000
Sample mean = 7.65
Sample variance = 2.61011
Sample maximum = 11
Sample minimum = 2
TEST135
For the Sech PDF:
SECH_CDF evaluates the CDF;
SECH_CDF_INV inverts the CDF.
SECH_PDF evaluates the PDF;
PDF parameter A = 3
PDF parameter B = 2
X PDF CDF CDF_INV
0.941182 0.100839 0.218418 0.941182
8.35531 0.0217727 0.956318 8.35531
5.58635 0.0812276 0.829509 5.58635
3.39009 0.156175 0.561695 3.39009
2.46147 0.153555 0.415307 2.46147
-1.52223 0.0328221 0.0661187 -1.52223
1.3038 0.115187 0.257578 1.3038
-0.492142 0.0538915 0.109957 -0.492142
-2.34859 0.0218453 0.043829 -2.34859
3.86774 0.145266 0.633966 3.86774
TEST136
For the Sech PDF:
SECH_MEAN computes the mean;
SECH_SAMPLE samples;
SECH_VARIANCE computes the variance;
PDF parameter A = 3
PDF parameter B = 2
PDF mean = 3
PDF variance = 9.8696
Sample size = 1000
Sample mean = 2.99951
Sample variance = 9.97628
Sample maximum = 14.4364
Sample minimum = -8.69458
TEST137
For the Semicircular PDF:
SEMICIRCULAR_CDF evaluates the CDF;
SEMICIRCULAR_CDF_INV inverts the CDF.
SEMICIRCULAR_PDF evaluates the PDF;
PDF parameter A = 3
PDF parameter B = 2
X PDF CDF CDF_INV
2.07408 0.282143 0.216167 2.07422
2.64915 0.313374 0.388897 2.64941
4.26118 0.247045 0.872972 4.26123
3.95508 0.27967 0.792025 3.95508
2.82894 0.317143 0.445615 2.8291
3.07844 0.318065 0.524963 3.07861
2.09106 0.283538 0.220968 2.09082
4.78579 0.143324 0.979302 4.78516
3.8562 0.287667 0.763967 3.85645
3.6144 0.302918 0.692448 3.61426
TEST138
For the Semicircular PDF:
SEMICIRCULAR_MEAN computes the mean;
SEMICIRCULAR_SAMPLE samples;
SEMICIRCULAR_VARIANCE computes the variance;
PDF parameter A = 3
PDF parameter B = 2
PDF mean = 3
PDF variance = 1
Sample size = 1000
Sample mean = 3.02688
Sample variance = 0.989554
Sample maximum = 4.96783
Sample minimum = 1.05174
TEST139:
STUDENT_CDF evaluates the cumulative density function
for the Student's T PDF.
STUDENT_CDF_VALUES returns some exact values.
A B C X Exact F STUDENT_CDF(A,B,C,X)
0 1 1 0.325 0.600023 0.600023
0 1 2 0.289 0.600108 0.600108
0 1 3 0.277 0.600115 0.600115
0 1 4 0.271 0.6001 0.6001
0 1 5 0.267 0.599934 0.599934
0 1 2 0.816 0.749886 0.749886
0 1 5 0.727 0.750088 0.750088
0 1 2 2.92 0.95 0.95
0 1 5 2.015 0.949997 0.949997
0 1 2 6.965 0.990001 0.990001
0 1 3 4.541 0.990002 0.990002
0 1 4 3.747 0.99 0.99
0 1 5 3.365 0.990001 0.990001
TEST140
For the Student PDF:
STUDENT_CDF evaluates the CDF;
STUDENT_PDF evaluates the PDF;
STUDENT_SAMPLE samples the PDF;
PDF parameter A = 0.5
PDF parameter B = 2
PDF parameter C = 6
X PDF CDF
1.23384 0.331326 0.636863
0.763175 0.37563 0.550194
0.320752 0.379419 0.465751
-2.11984 0.0746224 0.119069
0.50983 0.382723 0.501881
3.93888 0.0283131 0.931835
0.985322 0.359192 0.591825
-0.714645 0.259709 0.282948
0.144113 0.36986 0.432312
0.464835 0.382605 0.493271
TEST141
For the Student PDF:
STUDENT_MEAN evaluates the mean;
STUDENT_SAMPLE samples the PDF;
STUDENT_VARIANCE computes the variance;
PDF parameter A = 0.5
PDF parameter B = 2
PDF parameter C = 6
PDF mean = 0.5
PDF variance = 6
Sample size = 1000
Sample mean = 0.472733
Sample variance = 3.15695
Sample maximum = 12.2574
Sample minimum = -18.5475
TEST142
For the Noncentral Student PDF:
STUDENT_NONCENTRAL_CDF evaluates the CDF;
PDF argument X = 0.5
PDF parameter IDF = 10
PDF parameter B = 1
CDF value = 0.30528
TEST1425
TFN evaluates Owen's T function;
OWEN_VALUES returns some exact values;
H A T(H,A) Exact
0.0625 0.25 0.0389119 0.0389119
6.5 0.4375 2.00058e-11 2.00058e-11
7 0.96875 6.39906e-13 6.39906e-13
4.78125 0.0625 1.0633e-07 1.0633e-07
2 0.5 0.00862508 0.00862508
1 0.999997 0.0667418 0.0667418
1 0.5 0.0430647 0.0430647
1 1 0.0667419 0.0667419
1 2 0.0784682 0.0784682
1 3 0.0792995 0.0792995
0.5 0.5 0.0644886 0.0644886
0.5 1 0.106671 0.106671
0.5 2 0.141581 0.141581
0.5 3 0.151084 0.151084
0.25 0.5 0.0713466 0.0713466
0.25 1 0.120129 0.120129
0.25 2 0.166613 0.166613
0.25 3 0.18475 0.18475
0.125 0.5 0.0731727 0.0731727
0.125 1 0.123763 0.123763
0.125 2 0.173744 0.173744
0.125 3 0.195119 0.195119
0.0078125 0.5 0.0737894 0.0737894
0.0078125 1 0.124995 0.124995
0.0078125 2 0.176198 0.176198
0.0078125 3 0.198777 0.198777
0.0078125 10 0.234074 0.234089
0.0078125 100 0.233737 0.247946
TEST143
For the Triangle PDF:
TRIANGLE_CDF evaluates the CDF;
TRIANGLE_CDF_INV inverts the CDF.
TRIANGLE_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 3
PDF parameter C = 10
X PDF CDF CDF_INV
2.98281 0.220312 0.218418 2.98281
8.34109 0.0526639 0.956318 8.34109
6.72267 0.104042 0.829509 6.72267
4.74517 0.16682 0.561695 4.74517
3.93076 0.192674 0.415307 3.93076
2.09093 0.121215 0.0661187 2.09093
3.16095 0.217113 0.257578 3.16095
2.40685 0.156316 0.109957 2.40685
1.88821 0.0986903 0.043829 1.88821
5.1979 0.152448 0.633966 5.1979
TEST144
For the Triangle PDF:
TRIANGLE_MEAN computes the mean;
TRIANGLE_SAMPLE samples;
TRIANGLE_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 3
PDF parameter C = 10
PDF mean = 4.66667
PDF variance = 3.72222
Sample size = 1000
Sample mean = 4.67684
Sample variance = 3.70549
Sample maximum = 9.63699
Sample minimum = 1.18191
TEST145
For the Triangular PDF:
TRIANGULAR_CDF evaluates the CDF;
TRIANGULAR_CDF_INV inverts the CDF.
TRIANGULAR_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 10
X PDF CDF CDF_INV
3.97421 0.146875 0.218418 3.97421
8.66991 0.0656834 0.956318 8.66991
7.37229 0.129764 0.829509 7.37229
5.78677 0.208061 0.561695 5.78677
5.10121 0.202529 0.415307 5.10121
2.6364 0.0808099 0.0661187 2.6364
4.22985 0.159499 0.257578 4.22985
3.11027 0.104211 0.109957 3.11027
2.33232 0.0657935 0.043829 2.33232
6.14975 0.190136 0.633966 6.14975
TEST146
For the Triangular PDF:
TRIANGULAR_MEAN computes the mean;
TRIANGULAR_SAMPLE samples;
TRIANGULAR_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 10
PDF mean = 5.5
PDF variance = 3.375
Sample size = 1000
Sample mean = 5.51035
Sample variance = 3.38802
Sample maximum = 9.70895
Sample minimum = 1.27286
TEST147
For the Uniform 01 Order PDF:
UNIFORM_ORDER_SAMPLE samples.
Ordered sample:
1 0.0174736
2 0.0275623
3 0.131654
4 0.274807
5 0.385745
6 0.664103
7 0.768848
8 0.834884
9 0.854621
10 0.858873
TEST148
For the Uniform PDF on the N-Sphere:
UNIFORM_NSPHERE_SAMPLE samples.
Dimension N of sphere = 3
Points on the sphere:
1 0.781938 -0.263617 0.56487
2 0.413678 -0.542961 -0.730797
3 0.0544828 0.924277 -0.377813
4 0.723278 0.0995291 0.683347
5 0.747038 -0.663815 -0.035826
6 -0.78339 -0.516512 -0.34571
7 0.146773 0.598886 -0.78727
8 -0.649577 -0.399299 -0.647001
9 0.375237 -0.770087 0.51591
10 -0.408985 0.0579096 -0.910702
TEST1485
For the Uniform 01 PDF:
UNIFORM_01_CDF evaluates the CDF;
UNIFORM_01_CDF_INV inverts the CDF.
UNIFORM_01_PDF evaluates the PDF;
X PDF CDF CDF_INV
0.218418 1 0.218418 0.218418
0.956318 1 0.956318 0.956318
0.829509 1 0.829509 0.829509
0.561695 1 0.561695 0.561695
0.415307 1 0.415307 0.415307
0.0661187 1 0.0661187 0.0661187
0.257578 1 0.257578 0.257578
0.109957 1 0.109957 0.109957
0.043829 1 0.043829 0.043829
0.633966 1 0.633966 0.633966
TEST1486
For the Uniform 01 PDF:
UNIFORM_01_MEAN computes the mean;
UNIFORM_01_SAMPLE samples;
UNIFORM_01_VARIANCE computes the variance.
PDF mean = 0.5
PDF variance = 0.0833333
Sample size = 1000
Sample mean = 0.50304
Sample variance = 0.082332
Sample maximum = 0.997908
Sample minimum = 0.00183837
TEST149
For the Uniform PDF:
UNIFORM_CDF evaluates the CDF;
UNIFORM_CDF_INV inverts the CDF.
UNIFORM_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 10
X PDF CDF CDF_INV
2.96576 0.111111 0.218418 2.96576
9.60686 0.111111 0.956318 9.60686
8.46558 0.111111 0.829509 8.46558
6.05526 0.111111 0.561695 6.05526
4.73776 0.111111 0.415307 4.73776
1.59507 0.111111 0.0661187 1.59507
3.3182 0.111111 0.257578 3.3182
1.98961 0.111111 0.109957 1.98961
1.39446 0.111111 0.043829 1.39446
6.70569 0.111111 0.633966 6.70569
TEST150
For the Uniform PDF:
UNIFORM_MEAN computes the mean;
UNIFORM_SAMPLE samples;
UNIFORM_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 10
PDF mean = 5.5
PDF variance = 6.75
Sample size = 1000
Sample mean = 5.52736
Sample variance = 6.66889
Sample maximum = 9.98117
Sample minimum = 1.01655
TEST151
For the Uniform Discrete PDF:
UNIFORM_DISCRETE_CDF evaluates the CDF;
UNIFORM_DISCRETE_CDF_INV inverts the CDF.
UNIFORM_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 6
X PDF CDF CDF_INV
2 0.166667 0.333333 3
6 0.166667 1 6
6 0.166667 1 6
4 0.166667 0.666667 5
3 0.166667 0.5 4
1 0.166667 0.166667 2
3 0.166667 0.5 4
2 0.166667 0.333333 3
1 0.166667 0.166667 2
5 0.166667 0.833333 6
TEST152
For the Uniform Discrete PDF:
UNIFORM_DISCRETE_MEAN computes the mean;
UNIFORM_DISCRETE_SAMPLE samples;
UNIFORM_DISCRETE_VARIANCE computes the variance;
PDF parameter A = 1
PDF parameter B = 6
PDF mean = 3.5
PDF variance = 2.91667
Sample size = 1000
Sample mean = 3.945
Sample variance = 2.70068
Sample maximum = 6
Sample minimum = 1
TEST153
For the Uniform Discrete PDF:
UNIFORM_DISCRETE_CDF evaluates the CDF;
UNIFORM_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 6
X PDF CDF
0 0 0
1 0.166667 0.166667
2 0.166667 0.333333
3 0.166667 0.5
4 0.166667 0.666667
5 0.166667 0.833333
6 0.166667 1
7 0 1
8 0 1
9 0 1
10 0 1
TEST154
For the Von Mises PDF:
VON_MISES_CDF evaluates the CDF;
VON_MISES_CDF_INV inverts the CDF.
VON_MISES_PDF evaluates the PDF;
PDF parameter A = 1
PDF parameter B = 2
X PDF CDF CDF_INV
0.476234 0.394559 0.25232 0.476146
1.12227 0.50824 0.562764 1.12233
0.931772 0.51349 0.464857 0.931738
0.575338 0.43192 0.293305 0.575471
0.862805 0.506281 0.429664 0.862709
-1.39044 0.0161849 0.00863675 -1.39301
2.77511 0.0465295 0.974194 2.77328
0.193915 0.278813 0.157223 0.193893
0.786199 0.49292 0.391357 0.78601
0.790531 0.493818 0.393494 0.790612
TEST155
For the Von Mises PDF:
VON_MISES_MEAN computes the mean;
VON_MISES_SAMPLE samples;
VON_MISES_CIRCULAR_VARIANCE computes the circular variance;
PDF parameter A = 1
PDF parameter B = 2
PDF mean = 1
PDF circular variance = 0.302225
Sample size = 1000
Sample mean = 1.01316
Sample circular variance = 0.307398
Sample maximum = 4.0905
Sample minimum = -2.04316
TEST1555:
VON_MISES_CDF evaluates the von Mises CDF.
VON_MISES_CDF_VALUES returns some exact values.
A is the dominant angle;
B is a measure of spread;
X is the angle;
A B X Exact F Computed F
0 1 -2.61799 0.0253509 0.0253509
0 1 -1.5708 0.109754 0.109754
0 1 0 0.5 0.5
0 1 1.0472 0.804338 0.804338
0 1 2.0944 0.941746 0.941746
1 2 1 0.5 0.5
1 2 1.2 0.60182 0.60182
1 2 1.4 0.695936 0.695936
1 2 1.6 0.776594 0.776594
1 2 1.8 0.841073 0.841073
1 2 2 0.889578 0.889578
-2 3 0 0.996032 0.996032
-1 3 0 0.940434 0.940434
0 3 0 0.5 0.5
1 3 0 0.0595664 0.0595664
2 3 0 0.00396773 0.00396773
3 3 0 0.000232195 0.000232194
0 0 0.785398 0.625 0.625
0 1 0.785398 0.743841 0.743841
0 2 0.785398 0.836922 0.836922
0 3 0.785398 0.894171 0.894171
0 4 0.785398 0.929106 0.929106
0 5 0.785398 0.951429 0.951429
TEST156
For the Weibull PDF:
WEIBULL_CDF evaluates the CDF;
WEIBULL_CDF_INV inverts the CDF.
WEIBULL_PDF evaluates the PDF;
PDF parameter A = 2
PDF parameter B = 3
PDF parameter C = 4
X PDF CDF CDF_INV
4.11372 0.364494 0.218418 4.11372
5.99057 0.137084 0.956318 5.99057
5.45985 0.348698 0.829509 5.45985
4.859 0.505816 0.561695 4.859
4.56772 0.488817 0.415307 4.56772
3.53425 0.166552 0.0661187 3.53425
4.21624 0.399093 0.257578 4.21624
3.75263 0.236621 0.109957 3.75263
3.38034 0.124184 0.043829 3.38034
5.00376 0.489885 0.633966 5.00376
TEST157
For the Weibull PDF:
WEIBULL_MEAN computes the mean;
WEIBULL_SAMPLE samples;
WEIBULL_VARIANCE computes the variance.
PDF parameter A = 2
PDF parameter B = 3
PDF parameter C = 4
PDF mean = 4.71921
PDF variance = 0.581953
Sample size = 1000
Sample mean = 4.7225
Sample variance = 0.587748
Sample maximum = 6.72812
Sample minimum = 2.62134
TEST158
For the Weibull Discrete PDF:
WEIBULL_DISCRETE_CDF evaluates the CDF;
WEIBULL_DISCRETE_CDF_INV inverts the CDF.
WEIBULL_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 0.5
PDF parameter B = 1.5
X PDF CDF CDF_INV
0 0.5 0.5 0
2 0.113508 0.972723 2
1 0.359214 0.859214 1
1 0.359214 0.859214 1
0 0.5 0.5 0
0 0.5 0.5 0
0 0.5 0.5 0
0 0.5 0.5 0
0 0.5 0.5 0
1 0.359214 0.859214 1
TEST159
For the Weibull Discrete PDF:
WEIBULL_DISCRETE_CDF evaluates the CDF;
WEIBULL_DISCRETE_PDF evaluates the PDF;
PDF parameter A = 0.5
PDF parameter B = 1.5
X PDF CDF
0 0.5 0.5
1 0.359214 0.859214
2 0.113508 0.972723
3 0.0233711 0.996094
4 0.00347534 0.999569
5 0.000393254 0.999962
6 3.49916e-05 0.999997
7 2.50545e-06 1
8 1.46886e-07 1
9 7.14817e-09 1
10 2.91997e-10 1
TEST160
For the Weibull Discrete PDF:
WEIBULL_DISCRETE_SAMPLE samples;
PDF parameter A = 0.5
PDF parameter B = 1.5
Sample size = 1000
Sample mean = 0.676
Sample variance = 0.621646
Sample maximum = 4
Sample minimum = 0
TEST161
For the ZIPF PDF:
ZIPF_CDF evaluates the CDF;
ZIPF_PDF evaluates the PDF;
PDF parameter A = 2
X PDF CDF
1 0.607927 0.607927
2 0.151982 0.759909
3 0.0675475 0.827456
4 0.0379954 0.865452
5 0.0243171 0.889769
6 0.0168869 0.906656
7 0.0124067 0.919062
8 0.00949886 0.928561
9 0.00750527 0.936067
10 0.00607927 0.942146
11 0.00502419 0.94717
12 0.00422172 0.951392
13 0.0035972 0.954989
14 0.00310167 0.958091
15 0.0027019 0.960792
16 0.00237472 0.963167
17 0.00210355 0.965271
18 0.00187632 0.967147
19 0.00168401 0.968831
20 0.00151982 0.970351
TEST162
For the Zipf PDF:
ZIPF_MEAN computes the mean;
ZIPF_SAMPLE samples;
ZIPF_VARIANCE computes the variance.
PDF parameter A = 4
PDF mean = 1.11063
PDF variance = 0.286326
Sample size = 1000
Sample mean = 1.12
Sample variance = 0.197798
Sample maximum = 6
Sample minimum = 1
PROB_PRB
Normal end of execution.
18 September 2013 02:50:46 PM