The Cummulants and an Exact Expression of Generalized Logistic Distribution

Abstract

A generalization of the logistic distribution proposed by Prentice (1975) is very useful for approximating the continuoui distributions and for data analysis. In this paper, an expression for the rth cumulant of the generalization is derived. The generalized logistic (GL) distribution of Prentice (1975) can be expressed as an incomplete beta function. In particular when both shape parameters are integers, the cumulative GL distribution function can be simply expressed as a sum of binomial probabilities. The exact expression of the cumulative GL distribution function when one of the shape parameters is not an integer is derived.