scipy.stats.gennorm¶

scipy.stats.gennorm = <scipy.stats._continuous_distns.gennorm_gen object>[source]¶

A generalized normal continuous random variable.

As an instance of the rv_continuous class, gennorm object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

See also

laplace: Laplace distribution
norm: normal distribution

Notes

The probability density function for gennorm is [R613]:

                             beta
gennorm.pdf(x, beta) =  ---------------  exp(-|x|**beta)
                        2 gamma(1/beta)

gennorm takes \(\beta\) as a shape parameter. For \(\beta = 1\), it is identical to a Laplace distribution. For \beta = 2, it is identical to a normal distribution (with \(scale=1/\sqrt{2}\)).

References

[R613]

(1, 2) “Generalized normal distribution, Version 1”, https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

Examples

>>> from scipy.stats import gennorm
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> beta = 1.3
>>> mean, var, skew, kurt = gennorm.stats(beta, moments='mvsk')

Display the probability density function (pdf):

>>> x = np.linspace(gennorm.ppf(0.01, beta),
...                 gennorm.ppf(0.99, beta), 100)
>>> ax.plot(x, gennorm.pdf(x, beta),
...        'r-', lw=5, alpha=0.6, label='gennorm pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pdf:

>>> rv = gennorm(beta)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>> vals = gennorm.ppf([0.001, 0.5, 0.999], beta)
>>> np.allclose([0.001, 0.5, 0.999], gennorm.cdf(vals, beta))
True

Generate random numbers:

>>> r = gennorm.rvs(beta, size=1000)

And compare the histogram:

>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Methods

`rvs(beta, loc=0, scale=1, size=1, random_state=None)`	Random variates.
`pdf(x, beta, loc=0, scale=1)`	Probability density function.
`logpdf(x, beta, loc=0, scale=1)`	Log of the probability density function.
`cdf(x, beta, loc=0, scale=1)`	Cumulative distribution function.
`logcdf(x, beta, loc=0, scale=1)`	Log of the cumulative distribution function.
`sf(x, beta, loc=0, scale=1)`	Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate).
`logsf(x, beta, loc=0, scale=1)`	Log of the survival function.
`ppf(q, beta, loc=0, scale=1)`	Percent point function (inverse of `cdf` — percentiles).
`isf(q, beta, loc=0, scale=1)`	Inverse survival function (inverse of `sf`).
`moment(n, beta, loc=0, scale=1)`	Non-central moment of order n
`stats(beta, loc=0, scale=1, moments='mv')`	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
`entropy(beta, loc=0, scale=1)`	(Differential) entropy of the RV.
`fit(data, beta, loc=0, scale=1)`	Parameter estimates for generic data.
`expect(func, args=(beta,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)`	Expected value of a function (of one argument) with respect to the distribution.
`median(beta, loc=0, scale=1)`	Median of the distribution.
`mean(beta, loc=0, scale=1)`	Mean of the distribution.
`var(beta, loc=0, scale=1)`	Variance of the distribution.
`std(beta, loc=0, scale=1)`	Standard deviation of the distribution.
`interval(alpha, beta, loc=0, scale=1)`	Endpoints of the range that contains alpha percent of the distribution