1. Statistical Concepts
1.1 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 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
