Nick T. Thomopoulos

Statistical Distributions

Applications and Parameter Estimates

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-65111-8
• 1st ed. 2017
• Seitenzahl: 192
• Erscheinungstermin: 18. Oktober 2017
• Englisch
• Abmessung: 241mm x 160mm x 17mm
• Gewicht: 446g
• ISBN-13: 9783319651118
• ISBN-10: 3319651110
• Artikelnr.: 48654991

Autorenporträt

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. 

Inhaltsangabe

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

Rezensionen

"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)