Statistical Distributions

Applications and Parameter Estimates

  • Nick T.¬†Thomopoulos

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Nick T. Thomopoulos
    Pages 1-11
  3. Nick T. Thomopoulos
    Pages 13-19
  4. Nick T. Thomopoulos
    Pages 21-29
  5. Nick T. Thomopoulos
    Pages 31-38
  6. Nick T. Thomopoulos
    Pages 39-47
  7. Nick T. Thomopoulos
    Pages 49-58
  8. Nick T. Thomopoulos
    Pages 59-68
  9. Nick T. Thomopoulos
    Pages 69-76
  10. Nick T. Thomopoulos
    Pages 77-84
  11. Nick T. Thomopoulos
    Pages 85-95
  12. Nick T. Thomopoulos
    Pages 97-106
  13. Nick T. Thomopoulos
    Pages 107-112
  14. Nick T. Thomopoulos
    Pages 113-117
  15. Nick T. Thomopoulos
    Pages 119-126
  16. Nick T. Thomopoulos
    Pages 127-133
  17. Nick T. Thomopoulos
    Pages 135-141
  18. Nick T. Thomopoulos
    Pages 143-148
  19. Nick T. Thomopoulos
    Pages 149-152
  20. Nick T. Thomopoulos
    Pages 153-163
  21. Nick T. Thomopoulos
    Pages 165-169
  22. Back Matter
    Pages 171-172

About this book


This book gives a description of the group of statistical distributions that have ample application to studies in statistics and probability.  Understanding statistical distributions is fundamental for researchers in almost all disciplines.  The informed researcher will select the statistical distribution that best fits the data in the study at hand.  Some of the distributions are well known to the general researcher and are in use in a wide variety of ways.  Other useful distributions are less understood and are not in common use.  The book describes when and how to apply each of the distributions in research studies, with a goal to identify the distribution that best applies to the study.  The distributions are for continuous, discrete, and bivariate random variables.  In most studies, the parameter values are not known a priori, and sample data is needed to estimate parameter values.  In other scenarios, no sample data is available, and the researcher seeks some insight that allows the estimate of the parameter values to be gained.

This handbook of statistical distributions provides a working knowledge of applying common and uncommon statistical distributions in research studies.  These nineteen distributions are: continuous uniform, exponential, Erlang, gamma, beta, Weibull, normal, lognormal, left-truncated normal, right-truncated normal, triangular, discrete uniform, binomial, geometric, Pascal, Poisson, hyper-geometric, bivariate normal, and bivariate lognormal.  Some are from continuous data and others are from discrete and bivariate data.  This group of statistical distributions has ample application to studies in statistics and probability and practical use in real situations.  Additionally, this book explains computing the cumulative probability of each distribution and estimating the parameter values either with sample data or without sample data.  Examples are provided throughout to guide the reader.

Accuracy in choosing and applying statistical distributions is particularly imperative for anyone who does statistical and probability analysis, including management scientists, market researchers, engineers, mathematicians, physicists, chemists, economists, social science researchers, and students in many disciplines.

  • Includes 89 examples that help the reader apply the concepts presented
  • Explains how to compute cumulative probability for all distributions including Erlang, gamma, beta, Weibull, normal, and lognormal
  • Utilizes sample data to estimate parameter values of each distribution
  • Estimates parameter values when no sample data
  • Introduces Left-Truncated Normal
  • Introduces Right-Truncated Normal
  • Introduces Spread Ratio


bivariate normal bivariate lognormal Erlang Weibull distribution left-truncated normal right-truncated normal spread ratio probability statistical distributions parameter estimates maximum likelihood estimator

Authors and affiliations

  • Nick T.¬†Thomopoulos
    • 1
  1. 1.Stuart School of BusinessIllinois Institute of TechnologyBurr RidgeUSA

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