Statistical Distributions, Softcover reprint of the original 1st ed. 2017
Applications and Parameter Estimates

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Language: English

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Statistical Distributions
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Support: Print on demand

147.69 €

In Print (Delivery period: 15 days).

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Statistical Distributions
Publication date:
Support: Print on demand
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.

1.  Statistical Concepts

1.1 Introduction

Probability Distributions, Random Variables, Notation and Parameters

1.2 Fundamentals

1.3 Continuous Distribution

Admissible Range                           

Probability Density                         

Cumulative Distribution                               

Complementary Probability                       

Expected Value                               

Variance and Standard Deviation                             

Median                               

Coefficient-of-Variation                               

1.4 Discrete Distributions

Admissible Range                           

Probability Function                       

Cumulative Probability                 

Complementary Probability                       

Expected Value and Mean                          

Variance and Standard Deviation                             

Median                               

Mode                   

Lexis Ratio                          

1.5 Sample Data Basic Statistics

1.6 Parameter Estimating Methods

Maximum-Likelihood-Estimator  (MLE)

Method-of-Moments (MoM)

1.7 Transforming Variables                         

Transform Data to Zero or Larger

Transform Data to Zero and One                              

Continuous Distributions and Cov

Discrete Distributions and Lexis Ratio

1.8 Summary

2. Continuous Uniform

Fundamentals

Sample Data

Parameter Estimates from Sample Data

Parameter Estimates when No Data

When (a, b) Not Known

Summary

3. Exponential

Fundamentals

Table Values

Memory-Less Property

Poisson Relation

Sample Data

Parameter Estimate from Sample Data

Parameter Estimate when No Data

Summary

4. Erlang

Introduction

Fundamentals

Tables

Sample Data

Parameter Estimates when Sample Data

Parameter Estimates when No Data

Summary

5. Gamma

Introduction

Fundamentals

Gamma Function

Cumulative Probability

Estimating the Cumulative Probability

Sample Data

Parameter Estimates when Sample Data

Parameter Estimate when No Data

Summary

6. Beta

Introduction

Fundamentals

Standard Beta

Beta has Many Shapes

Sample Data

Parameter Estimates when Sample Data

Regression Estimate of the Mean from the Mode

Parameter Estimates when No Data

Summary

7. Weibull

Introduction

Fundamentals

Standard Weibull

Sample Data

Parameter Estimate of  when Sample Data

Parameter Estimate of (k1, k2) when Sample Data

Solving for k1                    

Solving for k2                    

Parameter Estimate when No Data

Summary

8. Normal

Introduction

Fundamentals

Standard Normal

Hastings Approximations

Approximation of F(z) from z     

Approximation of z from F(z)                     

Tables of the Standard Normal

Sample Data

Parameter Estimates when Sample Data

Parameter Estimates when No Data

Summary

9. Lognormal

Introduction

Fundamentals

Lognormal Mode

Lognormal Median

Sample Data

Parameter Estimates when Sample Data

Parameter Estimates when No Data

Summary

10. Left Truncated Normal

Introduction

Fundamentals

Standard Normal

Sample Data

Parameter Estimates when Sample Data

LTN in Inventory Control

Distribution Center in Auto Industry

Dealer, Retailer or Store

Summary

11. Right Truncated Normal

Introduction

Fundamentals

Standard Normal

Right-Truncated Normal

Cumulative Probability of k

Mean and Standard Deviation of t

Spread Ratio of RTN

Table Values

Sample Data

Parameter Estimates when Sample Data

Estimate  when RTN

Estimate the -percent-point of x

Summary

12. Triangular

Introduction

Fundamentals

Standard Triangular

Triangular

Parameter Estimates when No Data

Summary

13. Discrete Uniform

Introduction

Fundamentals

Lexis Ratio          

Sample Data

Parameter Estimates when Sample Data

Parameter Estimates when No Data

Summary

14. Binomial

Introduction

Fundamentals

Lexis Ratio

Normal Approximation                 

Poisson Approximation

Sample Data

Parameter Estimates with Sample Data

Parameter Estimates when No Data

Summary

15. Geometric

Introduction

Fundamentals

Number of Failures

Sample Data

Parameter Estimate with Sample Data

Number of Trials

Sample Data

Parameter Estimate with Sample Data

Parameter Estimate when No Sample Data

Lexis Ratio

Memory Less Property

Summary

16. Pascal

Introduction

Fundamentals

Number of Failures

Parameter Estimate when No Data

Number of Trials

Lexis Ratio

Parameter Estimate when Sample Data

Summary

17.  Poisson

Introduction

Fundamentals

Lexis Ratio

Parameter Estimate when Sample Data

Parameter Estimate when No Data

Exponential Connection

Summary

18. Hyper Geometric

Introduction

Fundamentals

Parameter Estimate when Sample Data

Binomial Estimate

Summary

19. Bivariate Normal

Introduction

Fundamentals

Bivariate Normal

Marginal Distributions

Conditional Distribution

Bivariate Standard Normal

Distributions

Approximation to the Cumulative Joint Probability

Statistical Tables

Summary

20. Bivariate Lognormal

Introduction

Fundamentals

Summary

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. 

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, Right-Truncated Normal and Spread Ratio

Includes supplementary material: sn.pub/extras