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.
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.
Albert W. Marshall, Professor Emeritus of Statistics at the University of British Colombia, previously served on the faculty of the University of Rochester and on the staff of the Boeing Scientific Research Laboratories. His fundamental contributions to reliability theory have had a profound effect in furthering its development. Ingram Olkin is Professor Emeritus of Statistics and Education at Stanford University, after having served on the faculties of Michigan State University and the University of Minnesota. He has made significant contributions in multivariate analysis and in the development of statistical methods in meta-analysis, which has resulted in its use in many applications. Professors Marshall and Olkin, coauthors of papers on inequalities, multivariate distributions, and matrix analysis, are about to celebrate 50 years of collaborations. Their basic book on majorization has promoted awareness of the subject, and led to new applications in such fields as economics, combinatorics, statistics, probability, matrix theory, chemistry, and political science.
From the reviews: "Life Distributions is supported by an extensive list of references, as well as a very helpful author and subject index. This book will become a standard reference on life distributions. Both academics and practitioners will no doubt enjoy it. It can serve as a textbook for presenting distributions and their properties, but more likely it will be used as a kind of encyclopedia for life distributions. " (Mario V. Wuthrich, American Statistical Association, JASA, March 2009, Vol. 104, No. 485) "Readership: Researchers, graduate students in statistics, mathematics or engineering ! . The purpose of the book is to study and classify various distributions for nonnegative random variables. ! The book gives an excellent survey of various types of families of distributions and provides a wide range of topics and examples. The proof of the results is given whenever needed. ! The value of the book lays in its encyclopedic nature: it gives a survey of hundreds of classifications and ordering methods." (E. Omey, Kwantitatieve Methoden, March, 2008) "The authors and their collaborators have a distinguished track record of research in this field and the book reflects this. For the student ! the book provides a wealth of material both for background facts and for further research. For the working statistician it explains connections between distributions that might be adopted as models for data ! ." (Martin Crowder, International Statistical Reviews, Vol. 76 (2), 2008) "The book under review is concerned mainly with univariate probability distributions for non-negative data. ! This is a reasonably well researched, fairly up-to-date book. The book emphasizes the interrelationship between various distributions covered here. ! A reader who has had a first course in probability and probability calculus will have no difficulty reading the book." (Gopalakrishnan Asha, Mathematical Reviews, Issue 2009 e)