# 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

 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)