Statistical Distributions
Applications and Parameter Estimates
(Sprache: Englisch)
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...
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Klappentext zu „Statistical Distributions “
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
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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.
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.
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Inhaltsverzeichnis zu „Statistical Distributions “
1. Statistical Concepts1.1 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
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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
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
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Autoren-Porträt von 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. Bibliographische Angaben
- Autor: Nick T. Thomopoulos
- 2018, Softcover reprint of the original 1st ed. 2017, XVII, 172 Seiten, 21 farbige Abbildungen, Maße: 15,6 x 23,3 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3319879529
- ISBN-13: 9783319879529
Sprache:
Englisch
Pressezitat
"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)
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