pearspdf

Pearson system probability distributions

% pearspdf
% [p,type,coefs] = pearspdf(X,mu,sigma,skew,kurt)
%
% Returns the probability distribution denisty of the pearsons distribution
% with mean `mu`, standard deviation `sigma`, skewness `skew` and
% kurtosis `kurt`, evaluated at the values in X.
%
% Some combinations of moments are not valid for any random variable, and in
% particular, the kurtosis must be greater than the square of the skewness
% plus 1. The kurtosis of the normal distribution is defined to be 3.
%
% The seven distribution types in the Pearson system correspond to the
% following distributions:
%
% Type 0: Normal distribution
% Type 1: Four-parameter beta
% Type 2: Symmetric four-parameter beta
% Type 3: Three-parameter gamma
% Type 4: Not related to any standard distribution. Density proportional
% to (1+((x-a)/b)^2)^(-c) * exp(-d*arctan((x-a)/b)).
% Type 5: Inverse gamma location-scale
% Type 6: F location-scale
% Type 7: Student's t location-scale
%
% Examples
%
% See also
% pearspdf pearsrnd mean std skewness kurtosis
%

It's a modification of the pearsrnd function