Probability Distributions: Truncated, Log and Bivariate Extensions

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 1.9 Erlang Parameter Estimates 1.10 Gamma Parameter Estimates 1.11 Beta Standard 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 1.16 Reference
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 Trials Lexis 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 Estimate2.9 Summary 2.10 Reference
3 Standard Normal 3.1 Introduction 3.2 Gaussian Distribution 3.3 Some Relations on the Standard Normal Distribution 4.3 Normal Distribution 3.5 Standard Normal 3.6 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 Distribution 3.9 Summary 3.10 References
4 Partial Expectation 4.1 Introduction 4.2 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 4.8 References
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 5.10 References
6 Right Truncated Normal 6.1 Introduction 6.2 Right Truncated Distribution 6.3 Mathematical Equations 6.4 Variable t Range 6.5 Table Entries 6.6 Application to Sample Data 6.7 More Tables 6.8 Summary 6.9 Reference
7 Truncated Normal Spread Ratio 7.1 Introduction 7.2 The Spread Ratio 7.3 LTN Distribution Measures7.4 LTN Table Entries 7.5 RTN Distribution Measures 7.6 RTN Table Entries 7.7 Estimating the Distribution Type 7.8 Selecting the Distribution Type 7.9 Estimating the Low and High Limits When LTN Estimate When LTN When RTN Estimate When RTN When Normal Compute the Adjusted Coefficient of Variation 7.10 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 Summary 8.7 References
9 Lognormal 9.1 Introduction 9.2 Lognormal Distribution 9.3 Notation 9.4 Lognormal Lognormal Mode Lognormal Median 9.5 Raw Lognormal Variable 9.6 Shifted Lognormal Variable 9.7 Normal Variable 9.8 Zero-Mean Normal Variable 9.9 Standard LN Variable 9.10 Lognormal Table Entries 9.11 Lognormal Distribution Table 9.12 Summary 9.13 Reference
10 Bivariate Lognormal 10.1 Introduction 10.2 Bivariate Lognormal Notation Some Properties Between x and y Mode of x and x` 10.3 Lognormal and Normal Notation Related Parameters 10.4 Bivariate Lognormal Distribution Bivariate Lognormal Correlation Bivariate Lognormal Designation 10.5 Bivariate Normal Distribution 10.6 Bivariate (Zero-Mean) Normal Distribution 10.7 Bivariate (Standard) Normal Distribution 10.8 Summary 10.9 References