Probability Models for Nonnegative Random Variables

Ingram Olkin
Stanford University

The normal distribution plays a central role as a model when random
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