scipy.stats.genpareto — SciPy v1.16.2 Manual (original) (raw)

scipy.stats.genpareto = <scipy.stats._continuous_distns.genpareto_gen object>[source]#

A generalized Pareto continuous random variable.

As an instance of the rv_continuous class, genpareto 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

Notes

The probability density function for genpareto is:

\[f(x, c) = (1 + c x)^{-1 - 1/c}\]

defined for \(x \ge 0\) if \(c \ge 0\), and for\(0 \le x \le -1/c\) if \(c < 0\).

genpareto takes c as a shape parameter for \(c\).

For \(c=0\), genpareto reduces to the exponential distribution, expon:

\[f(x, 0) = \exp(-x)\]

For \(c=-1\), genpareto is uniform on [0, 1]:

\[f(x, -1) = 1\]

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, genpareto.pdf(x, c, loc, scale) is identically equivalent to genpareto.pdf(y, c) / scale withy = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.

Examples

import numpy as np from scipy.stats import genpareto import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1)

Get the support:

c = 0.1 lb, ub = genpareto.support(c)

Calculate the first four moments:

mean, var, skew, kurt = genpareto.stats(c, moments='mvsk')

Display the probability density function (pdf):

x = np.linspace(genpareto.ppf(0.01, c), ... genpareto.ppf(0.99, c), 100) ax.plot(x, genpareto.pdf(x, c), ... 'r-', lw=5, alpha=0.6, label='genpareto 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 = genpareto(c) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

vals = genpareto.ppf([0.001, 0.5, 0.999], c) np.allclose([0.001, 0.5, 0.999], genpareto.cdf(vals, c)) True

Generate random numbers:

r = genpareto.rvs(c, 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()