Statistical Distributions

1. Front Matter

   Pages i-xvii

   PDF

2. Statistical Concepts

   • Nick T. Thomopoulos

   Pages 1-11

3. Continuous Uniform

   • Nick T. Thomopoulos

   Pages 13-19

4. Exponential

   • Nick T. Thomopoulos

   Pages 21-29

5. Erlang

   • Nick T. Thomopoulos

   Pages 31-38

6. Gamma

   • Nick T. Thomopoulos

   Pages 39-47

7. Beta

   • Nick T. Thomopoulos

   Pages 49-58

8. Weibull

   • Nick T. Thomopoulos

   Pages 59-68

9. Normal

   • Nick T. Thomopoulos

   Pages 69-76

10. Lognormal

    • Nick T. Thomopoulos

    Pages 77-84

11. Left Truncated Normal

    • Nick T. Thomopoulos

    Pages 85-95

12. Right Truncated Normal

    • Nick T. Thomopoulos

    Pages 97-106

13. Triangular

    • Nick T. Thomopoulos

    Pages 107-112

14. Discrete Uniform

    • Nick T. Thomopoulos

    Pages 113-117

15. Binomial

    • Nick T. Thomopoulos

    Pages 119-126

16. Geometric

    • Nick T. Thomopoulos

    Pages 127-133

17. Pascal

    • Nick T. Thomopoulos

    Pages 135-141

18. Poisson

    • Nick T. Thomopoulos

    Pages 143-148

19. Hyper Geometric

    • Nick T. Thomopoulos

    Pages 149-152

20. Bivariate Normal

    • Nick T. Thomopoulos

    Pages 153-163

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.

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

“The book is very reader-friendly written, with numerous numerical examples, clarifying graphs and explanations, and it can be useful for students, researchers, and practitioners applying statistics and probability evaluations in their studies.” (Stan Lipovetsky, Technometrics, Vol. 60 (2), 2018)​

• Stuart School of Business, Illinois Institute of Technology, Burr Ridge, USA

  Nick T. Thomopoulos

Nick T. Thomopoulos, Ph.D., has degrees in business (B.S.) and in mathematics (M.A.) from the University of Illinois, and in industrial engineering (Ph.D.) from Illinois Institute of Technology (Illinois Tech). He was supervisor of operations research at International Harvester; senior scientist at Illinois Tech Research Institute; Professor in Industrial Engineering, and in the Stuart School of Business at Illinois Tech. He is the author of eleven books including Fundamentals of Queuing Systems (Springer), Essentials of Monte Carlo Simulation (Springer), Applied Forecasting Methods (Prentice Hall), and Fundamentals of Production, Inventory and the Supply Chain (Atlantic). He has published many papers and has consulted in a wide variety of industries in the United States, Europe and Asia. Dr. Thomopoulos has received honors over the years, such as the Rist Prize from the Military Operations Research Society for new developments in queuing theory; the Distinguished Professor Award in Bangkok, Thailand from the Illinois Tech Asian Alumni Association; and the Professional Achievement Award from the Illinois Tech Alumni Association. 

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