# 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.

## 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 `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)