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.
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])	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.

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

Univariate Distributions by non-linear Transformations

Univariate distributions can be generated from a non-linear transformation of an existing univariate distribution. Transf_gen is a class that can generate a new distribution from a monotonic transformation, TransfTwo_gen can use hump-shaped or u-shaped transformation, such as abs or square. The remaining objects are special cases.

TransfTwo_gen(kls, func, funcinvplus, ...)	Distribution based on a non-monotonic (u- or hump-shaped transformation)
Transf_gen(kls, func, funcinv, *args, **kwargs)	a class for non-linear monotonic transformation of a continuous random variable
ExpTransf_gen(kls, *args, **kwargs)	Distribution based on log/exp transformation
LogTransf_gen(kls, *args, **kwargs)	Distribution based on log/exp transformation
SquareFunc()	class to hold quadratic function with inverse function and derivative
absnormalg	Distribution based on a non-monotonic (u- or hump-shaped transformation)
invdnormalg	a class for non-linear monotonic transformation of a continuous random variable
loggammaexpg	univariate distribution of a non-linear monotonic transformation of a random variable
lognormalg	a class for non-linear monotonic transformation of a continuous random variable
negsquarenormalg	Distribution based on a non-monotonic (u- or hump-shaped transformation)
squarenormalg	Distribution based on a non-monotonic (u- or hump-shaped transformation)
squaretg	Distribution based on a non-monotonic (u- or hump-shaped transformation)

Helper Functions

check_random_state([seed])

Turn seed into a random number generator.