Life Distributions

Structure of Nonparametric, Semiparametric, and Parametric Families

  • Albert W. Marshall
  • Ingram Olkin
Book
Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages I-XX
  2. Basics

    1. Front Matter
      Pages I-XX
    2. Albert W. Marshall, Ingram Olkin
      Pages 3-45
    3. Albert W. Marshall, Ingram Olkin
      Pages 47-77
    4. Albert W. Marshall, Ingram Olkin
      Pages 79-94
  3. Nonparametric Families

    1. Front Matter
      Pages I-XX
    2. Albert W. Marshall, Ingram Olkin
      Pages 97-136
    3. Albert W. Marshall, Ingram Olkin
      Pages 137-193
    4. Albert W. Marshall, Ingram Olkin
      Pages 195-214
  4. Semiparametric Families

    1. Front Matter
      Pages I-XX
    2. Albert W. Marshall, Ingram Olkin
      Pages 217-287
  5. Parametric Families

    1. Front Matter
      Pages I-XX
    2. Albert W. Marshall, Ingram Olkin
      Pages 291-307
    3. Albert W. Marshall, Ingram Olkin
      Pages 309-361
    4. Albert W. Marshall, Ingram Olkin
      Pages 363-398
    5. Albert W. Marshall, Ingram Olkin
      Pages 399-425
    6. Albert W. Marshall, Ingram Olkin
      Pages 427-449
    7. Albert W. Marshall, Ingram Olkin
      Pages 451-471
    8. Albert W. Marshall, Ingram Olkin
      Pages 473-495
    9. Albert W. Marshall, Ingram Olkin
      Pages 497-530

About this book

Introduction

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.
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. 

Keywords

Descriptive statistics Gaussian distribution Normal distribution Probability distribution Probability theory Survival analysis data analysis

Authors and affiliations

  • Albert W. Marshall
    • 1
  • Ingram Olkin
    • 2
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of StatisticsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68477-2
  • Copyright Information Springer 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Engineering
  • Print ISBN 978-0-387-20333-1
  • Online ISBN 978-0-387-68477-2
  • Series Print ISSN 0172-7397