A Review of Life Distributions

Abstract

Everything you ever wanted to know about distributions for non-negative random variables but were afraid to ask. This book is an amazing tome covering numerous distributions on the nonnegative real line. As the authors indicate in the preface, it is entirely about distributions and has no estimation theory. Readers should have a solid background in probability theory?the authors suggest a master's level in statistics?to make full use of the book. Important results, for example, the Glivenko-Cantelli theorem, various stochastic ordering results, log-concavity, or topics from real analysis and probability are discussed in a very readable way. The goal of the authors is to characterize strategies for construct ing probability distributions for the nonnegative real line. They do so by showing how many common distributions can arise from nonparametric, qualitative conditioning, that is, axiomatic, semiparametric, and fully parametric. Many common distributions can be derived from these four principles and the princi ples are illustrated using common distributions such as the exponential and its generalizations such as the gamma or Weibull, as well as lesser known distribu tions such as the logT family, which includes the log-normal and log-Cauchy as special cases. The primary use of life distributions in behavioral science is, of course, the study of reaction time, but many results also inform choice models. Much of this literature is highly technical and not always clearly related to the literature on survival analysis in biostatistics and sociology, which also make use of life distributions. Anyone wanting to get a strong hold on the technical literature in any of these areas would be greatly aided by this volume.