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. 

1. Continuous Distributions
1.1 Introduction1.2 Sample Data Statistics1.3 Notation1.4 Parameter Estimating Methods1.5 Transforming VariablesTransform Data to (0,1)Transform Data to (x 0)1.6 Continuous Random Variables1.7 Continuous Uniform Coefficient of VariationParameter Estimates1.8 Exponential 1.9 Erlang Parameter Estimates1.10 Gamma Parameter Estimates1.11 Beta Standard Beta Mean and Variance Parameter Estimates1.12  Weibull Weibull Plot Parameter Estimates1.13 NormalStandard Normal Distribution Coefficient of VariationParameter Estimates1.14 Lognormal   Parameter Estimates1.15 Summary1.16  Reference
2  Discrete Distributions2.1  Introduction2.2  Discrete Random VariablesLexis Ratio2.3  Discrete UniformParameter Estimates2.4  BinomialLexis RatioParameter EstimatesNormal Approximation Poisson Approximation 2.5 GeometricNumber of TrialsNumber of FailuresLexis RatioParameter Estimate2.6  PascalNumber of TrialsLexis Ratio Parameter EstimateNumber of FailuresLexis RatioParameter Estimate2.7  PoissonLexis RatioRelation to the Exponential DistributionParameter Estimate2.8  Hyper GeometricParameter Estimate2.9 Summary2.10  Reference
3 Standard Normal3.1 Introduction3.2 Gaussian Distribution3.3 Some Relations on the Standard Normal Distribution4.3 Normal Distribution3.5 Standard Normal3.6   Hastings ApproximationsApproximation of F(z) from zApproximation of z from F(z)3.7 Table Values of the Standard Normal3.8 Discrete Normal Distribution3.9 Summary3.10  References
4 Partial Expectation4.1 Introduction4.2 Partial Expectation4.3 Left Location ParameterTable Entries4.4 Inventory Management4.5 Right Location Parameter4.6 Advance Demand4.7  Summary4.8  References
5 Left Truncated Normal5.1  Introduction5.2  Left-Location Parameter5.3  Mathematical Equations5.4  Table Entries5.5  More Tables5.6  Left Truncated Distribution5.7 Application to Sample Data5.8  LTN for Inventory ControlAutomotive Service Parts Distribution CenterRetail Products5.9  Summary5.10  References
6  Right Truncated Normal6.1  Introduction6.2  Right Truncated Distribution6.3  Mathematical Equations6.4  Variable t Range6.5 Table Entries6.6 Application to Sample Data6.7  More Tables6.8  Summary6.9  Reference
7 Truncated Normal Spread Ratio7.1  Introduction7.2  The Spread Ratio7.3  LTN Distribution Measures7.4  LTN Table Entries7.5  RTN Distribution Measures7.6  RTN Table Entries7.7  Estimating the Distribution Type7.8  Selecting the Distribution Type7.9 Estimating the Low and High LimitsWhen LTNEstimate  When LTNWhen RTNEstimate When RTNWhen NormalCompute the Adjusted Coefficient of Variation7.10  Find xwhere P(x x) = 7.11  Find where P(x x`) = 7.12  Summary  
8  Bivariate Normal 8.1  Introduction 8.2  Bivariate Normal DistributionMarginal DistributionsConditional Distributions8.3  Bivariate Standard Normal DistributionConditional Distribution of z2Conditional Distribution of z1Cumulative Joint ProbabilityApproximation of F(k1,k2)Table Values of F(k1,k2) 8.4  Some Basic Probabilities for (z1,z2) ~ BVN(0,0,1,1,)8.5  Probabilities for (x1,x2) ~ BVN8.6  Summary8.7  References
9   Lognormal9.1 Introduction9.2  Lognormal Distribution9.3  Notation9.4  LognormalLognormal Mode Lognormal Median9.5  Raw Lognormal Variable9.6  Shifted Lognormal Variable9.7  Normal Variable9.8 Zero-Mean Normal Variable9.9 Standard LN Variable9.10 Lognormal Table Entries9.11 Lognormal Distribution Table9.12  Summary9.13  Reference
10 Bivariate Lognormal 10.1  Introduction10.2  Bivariate Lognormal   NotationSome Properties Between x and yMode of x and x`10.3  Lognormal and Normal NotationRelated Parameters10.4  Bivariate Lognormal DistributionBivariate Lognormal CorrelationBivariate Lognormal Designation10.5  Bivariate Normal Distribution10.6  Bivariate (Zero-Mean) Normal Distribution10.7  Bivariate (Standard) Normal Distribution10.8  Summary10.9  References