# scipy.stats.genpareto¶

scipy.stats.genpareto

A generalized Pareto continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters : x : array-like quantiles q : array-like lower or upper tail probability c : array-like shape parameters loc : array-like, optional location parameter (default=0) scale : array-like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape, : location, and scale parameters returning a “frozen” continuous RV object: : rv = genpareto(c, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Generalized Pareto distribution

genpareto.pdf(x,c) = (1+c*x)**(-1-1/c) for c != 0, and for x >= 0 for all c, and x < 1/abs(c) for c < 0.

Examples

>>> import matplotlib.pyplot as plt
>>> numargs = genpareto.numargs
>>> [ c ] = [0.9,] * numargs
>>> rv = genpareto(c)

Display frozen pdf

>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))

Check accuracy of cdf and ppf

>>> prb = genpareto.cdf(x, c)
>>> h = plt.semilogy(np.abs(x - genpareto.ppf(prb, c)) + 1e-20)

Random number generation

>>> R = genpareto.rvs(c, size=100)

Methods

 rvs(c, loc=0, scale=1, size=1) Random variates. pdf(x, c, loc=0, scale=1) Probability density function. cdf(x, c, loc=0, scale=1) Cumulative density function. sf(x, c, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate). ppf(q, c, loc=0, scale=1) Percent point function (inverse of cdf — percentiles). isf(q, c, loc=0, scale=1) Inverse survival function (inverse of sf). stats(c, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(c, loc=0, scale=1) (Differential) entropy of the RV. fit(data, c, loc=0, scale=1) Parameter estimates for generic data.

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