scipy.stats.rv_continuous.fit¶
-
rv_continuous.
fit
(data, *args, **kwds)[source]¶ Return MLEs for shape (if applicable), location, and scale parameters from data.
MLE stands for Maximum Likelihood Estimate. Starting estimates for the fit are given by input arguments; for any arguments not provided with starting estimates,
self._fitstart(data)
is called to generate such.One can hold some parameters fixed to specific values by passing in keyword arguments
f0
,f1
, …,fn
(for shape parameters) andfloc
andfscale
(for location and scale parameters, respectively).Parameters: data : array_like
Data to use in calculating the MLEs.
args : floats, optional
Starting value(s) for any shape-characterizing arguments (those not provided will be determined by a call to
_fitstart(data)
). No default value.kwds : floats, optional
Starting values for the location and scale parameters; no default. Special keyword arguments are recognized as holding certain parameters fixed:
- f0…fn : hold respective shape parameters fixed.
Alternatively, shape parameters to fix can be specified by name.
For example, if
self.shapes == "a, b"
,fa``and ``fix_a
are equivalent tof0
, andfb
andfix_b
are equivalent tof1
. - floc : hold location parameter fixed to specified value.
- fscale : hold scale parameter fixed to specified value.
- optimizer : The optimizer to use. The optimizer must take
func
, and starting position as the first two arguments, plusargs
(for extra arguments to pass to the function to be optimized) anddisp=0
to suppress output as keyword arguments.
Returns: mle_tuple : tuple of floats
MLEs for any shape parameters (if applicable), followed by those for location and scale. For most random variables, shape statistics will be returned, but there are exceptions (e.g.
norm
).Notes
This fit is computed by maximizing a log-likelihood function, with penalty applied for samples outside of range of the distribution. The returned answer is not guaranteed to be the globally optimal MLE, it may only be locally optimal, or the optimization may fail altogether.
Examples
Generate some data to fit: draw random variates from the
beta
distribution>>> from scipy.stats import beta >>> a, b = 1., 2. >>> x = beta.rvs(a, b, size=1000)
Now we can fit all four parameters (
a
,b
,loc
andscale
):>>> a1, b1, loc1, scale1 = beta.fit(x)
We can also use some prior knowledge about the dataset: let’s keep
loc
andscale
fixed:>>> a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1) >>> loc1, scale1 (0, 1)
We can also keep shape parameters fixed by using
f
-keywords. To keep the zero-th shape parametera
equal 1, usef0=1
or, equivalently,fa=1
:>>> a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1) >>> a1 1
Not all distributions return estimates for the shape parameters.
norm
for example just returns estimates for location and scale:>>> from scipy.stats import norm >>> x = norm.rvs(a, b, size=1000, random_state=123) >>> loc1, scale1 = norm.fit(x) >>> loc1, scale1 (0.92087172783841631, 2.0015750750324668)
- f0…fn : hold respective shape parameters fixed.
Alternatively, shape parameters to fix can be specified by name.
For example, if