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.

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.

Last update: Oct 03, 2024