# 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.

## Distribution Extras¶

Skew Distributions

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

Distributions based on Gram-Charlier expansion

 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. 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)