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Statistical Distributions: Applications and Parameter Estimates


Statistical Distributions: Applications and Parameter Estimates
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Beschreibung

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

Eigenschaften

Breite: 156
Gewicht: 302 g
Höhe: 233
Länge: 11
Seiten: 172
Sprachen: Englisch
Autor: Nick T. Thomopoulos

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