Probability Distributions : Truncated, Log and Bivariate Extensions (SpringerBriefs in Statistics) （1st ed. 2017. 2017. x, 100 S. 32 SW-Abb. 235 mm）

Thomopoulos, Nick T.

SPRINGER, BERLIN; SPRINGER INTERNATIONAL PUBLISHING;（2017発売）

• 製本 Paperback:紙装版/ペーパーバック版
• 商品コード 9783319519715

Full Description

This unique SpringerBrief presents 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.

Contents

1. Continuous Distributions1.1 Introduction1.2 Sample Data Statistics1.3 Notation1.4 Parameter Estimating Methods1.5 Transforming Variables Transform Data to (0,1) Transform Data to (x 0) 1.6 Continuous Random Variables1.7 Continuous Uniform Coefficient of Variation Parameter 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 Normal Standard Normal Distribution Coefficient of Variation Parameter Estimates1.14 Lognormal Parameter Estimates1.15 Summary1.16 Reference2 Discrete Distributions2.1 Introduction2.2 Discrete Random Variables Lexis Ratio2.3 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 Estimate2.6 Pascal Number of Trials Lexis Ratio Parameter Estimate Number of Failures Lexis Ratio Parameter Estimate2.7 Poisson Lexis Ratio Relation to the Exponential Distribution Parameter Estimate2.8 Hyper Geometric Parameter Estimate2.9 Summary2.10 Reference3 Standard Normal3.1 Introduction3.2 Gaussian Distribution 3.3 Some Relations on the Standard Normal Distribution4.3 Normal Distribution3.5 Standard Normal3.6 Hastings Approximations Approximation of F(z) from z Approximation of z from F(z) 3.7 Table Values of the Standard Normal 3.8 Discrete Normal Distribution3.9 Summary3.10 References4 Partial Expectation4.1 Introduction4.2 Partial Expectation4.3 Left Location Parameter Table Entries4.4 Inventory Management4.5 Right Location Parameter4.6 Advance Demand4.7 Summary4.8 References5 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 Control Automotive Service Parts Distribution Center Retail Products5.9 Summary5.10 References6 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 Reference7 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 Limits When LTN Estimate When LTN When RTN Estimate When RTN When Normal Compute the Adjusted Coefficient of Variation7.10 Find x where P(x x ) = 7.11 Find where P(x x`) = 7.12 Summary 8 Bivariate Normal 8.1 Introduction 8.2 Bivariate Normal Distribution Marginal Distributions Conditional Distributions 8.3 Bivariate Standard Normal Distribution Conditional Distribution of z2 Conditional Distribution of z1 Cumulative Joint Probability Approximation 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) ‾ BVN 8.6 Summary8.7 References9 Lognormal9.1 Introduction9.2 Lognormal Distribution9.3 Notation9.4 Lognormal Lognormal 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 Reference10 Bivariate Lognormal 10.1 Introduction10.2 Bivariate Lognormal Notation Some Properties Between x and y Mode of x and x`10.3 Lognormal and Normal Notation Related Parameters10.4 Bivariate Lognormal Distribution Bivariate Lognormal Correlation Bivariate Lognormal Designation10.5 Bivariate Normal Distribution10.6 Bivariate (Zero-Mean) Normal Distribution10.7 Bivariate (Standard) Normal Distribution10.8 Summary10.9 References