Distributions

This section collects various additional functions and methods for statistical distributions.

Empirical Distributions

ECDF(x[, side])	Return the Empirical CDF of an array as a step function.
ECDFDiscrete(x[, freq_weights, side])	Return the Empirical Weighted CDF of an array as a step function.
StepFunction(x, y[, ival, sorted, side])	A basic step function.
monotone_fn_inverter(fn, x[, vectorized])	Given a monotone function fn (no checking is done to verify monotonicity) and a set of x values, return an linearly interpolated approximation to its inverse from its values on x.

Count Distributions

The discrete module contains classes for count distributions that are based on discretizing a continuous distribution, and specific count distributions that are not available in scipy.distributions like generalized poisson and zero-inflated count models.

The latter are mainly in support of the corresponding models in statsmodels.discrete. Some methods are not specifically implemented and will use potentially slow inherited generic methods.

DiscretizedCount(*args, **kwds)	Count distribution based on discretized distribution
DiscretizedModel(endog[, exog, distr])	experimental model to fit discretized distribution
genpoisson_p	Generalized Poisson distribution
zigenpoisson	Zero Inflated Generalized Poisson distribution
zinegbin	Zero Inflated Generalized Negative Binomial distribution
zipoisson	Zero Inflated Poisson distribution

Copula

The copula sub-module provides classes to model the dependence between parameters. Copulae are used to construct a multivariate joint distribution and provide a set of functions like sampling, PDF, CDF.

CopulaDistribution(copula, marginals[, cop_args])	Multivariate copula distribution
ArchimedeanCopula(transform[, args, k_dim])	Base class for Archimedean copulas
FrankCopula([theta, k_dim])	Frank copula.
ClaytonCopula([theta, k_dim])	Clayton copula.
GumbelCopula([theta, k_dim])	Gumbel copula.
GaussianCopula([corr, k_dim, allow_singular])	Gaussian copula.
StudentTCopula([corr, df, k_dim])	Student t copula.
ExtremeValueCopula(transform[, args, k_dim])	Extreme value copula constructed from Pickand's dependence function.
IndependenceCopula([k_dim])	Independence copula.
rvs_kernel(sample, size[, bw, k_func, ...])	Random sampling from empirical copula using Beta distribution

The Archimedean generator transforms used by ArchimedeanCopula and the Pickands dependence functions used by ExtremeValueCopula are in

and

respectively.

Bernstein Distribution

Univariate and bivariate distributions estimated nonparametrically on the unit hypercube using Bernstein polynomials, e.g. for use as the marginal or copula component of a semiparametric model.

BernsteinDistribution(cdf_grid)	Distribution based on Bernstein Polynomials on unit hypercube.
BernsteinDistributionUV(cdf_grid)
BernsteinDistributionBV(cdf_grid)

Mixture of Distributions

Tools for combining component distributions into a mixture and generating random samples from the mixture.

MixtureDistribution()	univariate mixture distribution
mixture_rvs(prob, size, dist[, kwargs, rng])	Sample from a mixture of distributions.
mv_mixture_rvs(prob, size, dist, nvars[, rng])	Sample from a mixture of multivariate distributions.

Distribution Extras

Skew Distributions

SkewNorm_gen()	univariate Skew-Normal distribution of Azzalini
SkewNorm2_gen([momtype, a, b, xtol, ...])	univariate Skew-Normal distribution of Azzalini
ACSkewT_gen()	univariate Skew-T distribution of Azzalini
skewnorm2	univariate Skew-Normal distribution of Azzalini

Distributions based on Gram-Charlier expansion

pdf_moments_st(cnt)	Return the Gaussian expanded pdf function given the list of central moments (first one is mean).
pdf_mvsk(mvsk)	Return the Gaussian expanded pdf function given the list of 1st, 2nd moment and skew and Fisher (excess) kurtosis.
pdf_moments(cnt)	Return the Gaussian expanded pdf function given the list of central moments (first one is mean).
NormExpan_gen(args, **kwds)	Gram-Charlier Expansion of Normal distribution

cdf of multivariate normal wrapper for scipy.stats

mvstdnormcdf(lower, upper, corrcoef, **kwds)	standardized multivariate normal cumulative distribution function
mvnormcdf(upper, mu, cov[, lower])	multivariate normal cumulative distribution function

Helper Functions

check_random_state([seed, deprecated, warn])

Turn a seed into a random number generator