The S-Distribution: Approximation of Discrete Distributions

The S-distribution is defined by the ordinary differential equation dF/dX = α(F^g — F^h F_o = F(X_o), where F is the cumulative distribution of the random variable X, and α, g, h, and F_o are parameters. The S-distribution was recently described in this journal as a tool for the approximation and classification of univariate, unimodal continuous probability distributions. This article shows that the S-distribution rather accurately models the commonly used univariate discrete distributions.