For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families-nonparametric, semiparametric and parametric-some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data.
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.
Preliminaries.- Ordering distributions: Descriptive statistics.- Mixtures .- Nonparametric families: densities and hazard rates.- Nonparametric families: origins in reliability theory.- Nonparametric famlies: inequalities for moments and survival functions.- Semiparametric families.- Exponential distributions.- Parametric extensions of the exponential distribution.- Gompertz and Gompertz-Makeham distributions- Pareto and F distributions and their parametric extensions.- Logarithmic distributions.- Inverse Gaussian distributions.- Distributions with bounded support.- Additional parametric families.- Covariate models.- Several types of failure; competing risks.- Characterizations through coincidences of semiparametric families.- More about semiparametric families.- Some topics from probability theory.- Convexity and total positivity.- Functional equations.- The Gamma and Beta functions.- Some topics from calculus and analysis.
'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.
