The normal distribution plays a central role as a model when randomProbability Models for Nonnegative Random Variables

Ingram OlkinStanford University

variables take both negative and positive values. But for nonnegative

random variables there is no distribution as pervasive as the normal

distribution with its foundation in the Central Limit Theorem. This

means that a wide variety of distribution share relative importance.

In this survey we discuss (1) alternative descriptions of distributions,

(2) ordering of distributions, (3) nonparametric families, (4) semiparametric

families, (5) covariate models, (6) coincidences of families.This is joint work with A. W. Marshall