Distributions¶
This section collects various additional functions and methods for statistical distributions.
Empirical Distributions¶

Return the Empirical CDF of an array as a step function. 

A basic step function. 

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 zeroinflated 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.

Count distribution based on discretized distribution 

experimental model to fit discretized distribution 
Generalized Poisson distribution 

Zero Inflated Generalized Poisson distribution 

Zero Inflated Generalized Negative Binomial distribution 

Zero Inflated Poisson distribution 
Distribution Extras¶
Skew Distributions
univariate SkewNormal distribution of Azzalini 


univariate SkewNormal distribution of Azzalini 
univariate SkewT distribution of Azzalini 

univariate SkewNormal distribution of Azzalini 
Distributions based on GramCharlier expansion

Return the Gaussian expanded pdf function given the list of central moments (first one is mean). 

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). 

GramCharlier Expansion of Normal distribution 
cdf of multivariate normal wrapper for scipy.stats

standardized multivariate normal cumulative distribution function 

multivariate normal cumulative distribution function 
Univariate Distributions by nonlinear Transformations¶
Univariate distributions can be generated from a nonlinear 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 humpshaped or ushaped transformation, such as abs or square. The remaining objects are special cases.

Distribution based on a nonmonotonic (u or humpshaped transformation) 

a class for nonlinear monotonic transformation of a continuous random variable 

Distribution based on log/exp transformation 

Distribution based on log/exp transformation 
class to hold quadratic function with inverse function and derivative 

Distribution based on a nonmonotonic (u or humpshaped transformation) 

a class for nonlinear monotonic transformation of a continuous random variable 

univariate distribution of a nonlinear monotonic transformation of a random variable 

a class for nonlinear monotonic transformation of a continuous random variable 

Distribution based on a nonmonotonic (u or humpshaped transformation) 

Distribution based on a nonmonotonic (u or humpshaped transformation) 

Distribution based on a nonmonotonic (u or humpshaped transformation) 