Probability distributions : with truncated, log and bivariate extensions / Nick T. Thomopoulos.
Thomopoulos, Nicholas T., author.
2018
QA273.6
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Title Probability distributions : with truncated, log and bivariate extensions / Nick T. Thomopoulos.
Author Thomopoulos, Nicholas T., author.
ISBN 9783319760421 (electronic book)
3319760424 (electronic book)
9783319760414
DOI https://doi.org/10.1007/978-3-319-76042-1
Published Cham : Springer, 2018.
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-76042-1 doi
Call Number QA273.6
Dewey Decimal Classification 519.24
Summary This volume presents a concise and practical overview of statistical methods and tables not readily available in other publications. It begins with a review of the commonly used continuous and discrete probability distributions. Several useful distributions that are not so common and less understood are described with examples and applications in full detail: discrete normal, left-partial, right-partial, left-truncated normal, right-truncated normal, lognormal, bivariate normal, and bivariate lognormal. Table values are provided with examples that enable researchers to easily apply the distributions to real applications and sample data. The left- and right-truncated normal distributions offer a wide variety of shapes in contrast to the symmetrically shaped normal distribution, and a newly developed spread ratio enables analysts to determine which of the three distributions best fits a particular set of sample data. The book will be highly useful to anyone who does statistical and probability analysis. This includes scientists, economists, management scientists, market researchers, engineers, mathematicians, and students in many disciplines. 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 the IIT Research Institute; and 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.-- Provided by publisher.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (viewed April 16, 2018).
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Intro; In Memory of Nick T. Thomopoulos; Preface; Acknowledgments; Contents; About the Author; Chapter 1: Continuous Distributions; 1.1 Introduction; 1.2 Sample Data Statistics; 1.3 Notation; 1.4 Parameter Estimating Methods; 1.5 Transforming Variables; Transform Data to (0,1); Transform Data to (x 0); 1.6 Continuous Random Variables; 1.7 Continuous Uniform; Coefficient of Variation; Parameter Estimates; 1.8 Exponential; Parameter Estimate; 1.9 Erlang; Coefficient-of-Variation; Parameter Estimates; Cumulative Probability; 1.10 Gamma; Parameter Estimates; Cumulative Probability Estimates

1.11 BetaStandard Beta; Mean and Variance; Parameter Estimates; 1.12 Weibull; Weibull Plot; Parameter Estimates; 1.13 Normal; Standard Normal Distribution; Coefficient of Variation; Parameter Estimates; 1.14 Lognormal; Parameter Estimates; 1.15 Summary; References; Chapter 2: Discrete Distributions; 2.1 Introduction; 2.2 Discrete Random Variables; Lexis Ratio; 2.3 Discrete Uniform; Parameter Estimates; 2.4 Binomial; Lexis Ratio; Parameter Estimates; Normal Approximation; Poisson Approximation; 2.5 Geometric; Number of Trials; Number of Failures; Lexis Ratio; Parameter Estimate; 2.6 Pascal

Number of TrialsLexis Ratio; Parameter Estimate; Number of Failures; Lexis Ratio; Parameter Estimate; 2.7 Poisson; Lexis Ratio; Relation to the Exponential Distribution; Parameter Estimate; 2.8 Hyper Geometric; Parameter Estimate; 2.9 Summary; References; Chapter 3: Standard Normal; 3.1 Introduction; 3.2 Gaussian Distribution; 3.3 Some Relations on the Standard Normal Distribution; 3.4 Normal Distribution; 3.5 Standard Normal; 3.6 Hastings Approximations; 3.7 Table Values of the Standard Normal; 3.8 Discrete Normal Distribution; 3.9 Summary; References; Chapter 4: Partial Expectation

4.1 Introduction4.2 Partial Expectation; 4.3 Left Location Parameter; Table Entries; 4.4 Inventory Management; 4.5 Right Location Parameter; 4.6 Advance Demand; 4.7 Summary; References; Chapter 5: Left Truncated Normal; 5.1 Introduction; 5.2 Left-Location Parameter; 5.3 Mathematical Equations; 5.4 Table Entries; 5.5 More Tables; 5.6 Left Truncated Distribution; 5.7 Application to Sample Data; 5.8 LTN for Inventory Control; Automotive Service Parts Distribution Center; Retail Products; 5.9 Summary; References; Chapter 6: Right Truncated Normal; 6.1 Introduction

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