This book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.

InhaltsangabeBasics.- Preliminaries.- Ordering Distributions: Descriptive Statistics.- Mixtures.- Nonparametric Families.- Nonparametric Families: Densities and Hazard Rates.- Nonparametric Families: Origins in Reliability Theory.- Nonparametric Families: Inequalities for Moments and Survival Functions.- Semiparametric Families.- Semiparametric Families.- Parametric Families.- The Exponential Distribution.- Parametric Extensions of the Exponential Distribution.- Gompertz and Gompertz-Makeham Distributions.- The Pareto and F Distributions and Their Parametric Extensions.- Logarithmic Distributions.- The Inverse Gaussian Distribution.- Distributions with Bounded Support.- Additional Parametric Families.- Models Involving Several Variables.- Covariate Models.- Several Types of Failure: Competing Risks.- More About Semi-parametric Families.- Characterizations Through Coincidences of Semiparametric Families.- More About Semiparametric Families.- Complementary Topics.- Some Topics from Probability Theory.- Convexity and Total Positivity.- Some Functional Equations.- Gamma and Beta Functions.- Some Topics from Analysis.