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Module « scipy.stats »

Fonction gennorm - module scipy.stats

Signature de la fonction gennorm

def gennorm(*args, **kwds) 

Description

help(scipy.stats.gennorm)

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.

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(order, beta, loc=0, scale=1)
    Non-central moment of the specified order.
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)
    Parameter estimates for generic data.
    See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
    keyword arguments.
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(confidence, beta, loc=0, scale=1)
    Confidence interval with equal areas around the median.

See Also
--------
laplace : Laplace distribution
norm : normal distribution

Notes
-----
The probability density function for `gennorm` is [1]_:

.. math::

    f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta),

where :math:`x` is a real number, :math:`\beta > 0` and
:math:`\Gamma` is the gamma function (`scipy.special.gamma`).

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

References
----------

.. [1] "Generalized normal distribution, Version 1",
       https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

.. [2] Nardon, Martina, and Paolo Pianca. "Simulation techniques for
       generalized Gaussian densities." Journal of Statistical
       Computation and Simulation 79.11 (2009): 1317-1329

.. [3] Wicklin, Rick. "Simulate data from a generalized Gaussian
       distribution" in The DO Loop blog, September 21, 2016,
       https://blogs.sas.com/content/iml/2016/09/21/simulate-generalized-gaussian-sas.html

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

Calculate the first four 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, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

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