scipy.stats.genextreme

scipy.stats.genextreme = <scipy.stats._continuous_distns.genextreme_gen object>

A generalized extreme value continuous random variable.

As an instance of the rv_continuous class, genextreme 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(c, loc=0, scale=1, size=1, random_state=None)	Random variates.
pdf(x, c, loc=0, scale=1)	Probability density function.
logpdf(x, c, loc=0, scale=1)	Log of the probability density function.
cdf(x, c, loc=0, scale=1)	Cumulative distribution function.
logcdf(x, c, loc=0, scale=1)	Log of the cumulative distribution function.
sf(x, c, loc=0, scale=1)	Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
logsf(x, c, loc=0, scale=1)	Log of the survival function.
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).
moment(order, c, loc=0, scale=1)	Non-central moment of the specified order.
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)	Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.
expect(func, args=(c,), 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(c, loc=0, scale=1)	Median of the distribution.
mean(c, loc=0, scale=1)	Mean of the distribution.
var(c, loc=0, scale=1)	Variance of the distribution.
std(c, loc=0, scale=1)	Standard deviation of the distribution.
interval(confidence, c, loc=0, scale=1)	Confidence interval with equal areas around the median.

See also

gumbel_r

Notes

For \(c=0\), genextreme is equal to gumbel_r with probability density function

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

where \(-\infty < x < \infty\).

For \(c \ne 0\), the probability density function for genextreme is:

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

where \(-\infty < x \le 1/c\) if \(c > 0\) and \(1/c \le x < \infty\) if \(c < 0\).

Note that several sources and software packages use the opposite convention for the sign of the shape parameter \(c\).