Basics.- 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.
Über den Autor
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.
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.
PThis 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./P
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.