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Table of Contents
Preface; Contents; 1 Accurate Estimation with One Order Statistic; 1.1 Introduction; 1.2 The Case of the Exponential Distribution; 1.3 An Example for the Exponential Distribution; 1.4 The Rayleigh and Weibull Distribution Extensions; 1.5 Simulations and Computational Issues; 1.6 Implications for Design of Life Tests; 1.7 Conclusions; 2 On the Inverse Gamma as a Survival Distribution ; 2.1 Introduction; 2.2 Probabilistic Properties; 2.3 Statistical Inference; 2.3.1 Complete Data Sets; 2.3.2 Censored Data Sets; 2.4 Conclusions; 3 Order Statistics in Goodness-of-Fit Testing ; 3.1 Introduction.
3.2 P-Vector3.3 Computation of the P-Vector ; 3.4 Goodness-of-Fit Testing; 3.5 Power Estimates for Test Statistics; 3.6 Further Research; 4 The ``Straightforward'' Nature of Arrival Rate Estimation?; 4.1 Introduction; 4.1.1 Sampling Plan 1: Time Sampling; 4.1.2 Sampling Plan 2: Count Sampling; 4.1.3 Sampling Plan 3: Limit Both Time and Arrivals; 4.2 Conclusions; 5 Survival Distributions Based on the Incomplete Gamma Function Ratio ; 5.1 Introduction; 5.2 Properties and Results; 5.3 Examples; 5.4 Conclusions.
6 An Inference Methodology for Life Tests with Full Samples or Type II Right Censoring 6.1 Introduction and Literature Review; 6.2 The Methodology for Censored Data; 6.3 The Uniformity Test Statistic; 6.4 Implementation Using APPL; 6.5 Power Simulation Results; 6.6 Some Applications and Implications; 6.7 Conclusions and Further Research; 7 Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics ; 7.1 Introduction; 7.2 MLEOS with Complete Samples; 7.3 Applying MLEOS to Censored Samples; 7.4 Conclusions and Further Research; 8 Notes on Rank Statistics.
8.1 Introduction8.2 Explanation of the Tests; 8.3 Distribution of the Test Statistic Under H0; 8.4 Wilcoxon Power Curves for n = 2; 8.5 Generalization to Larger Sample Sizes; 8.6 Comparisons and Analysis; 8.7 The Wilcoxon-Mann-Whitney Test; 8.8 Explanation of the Test; 8.9 Three Cases of the Distribution of W Under H0; 8.9.1 Case I: No Ties; 8.9.2 Case II: Ties Only Within Each Sample; 8.9.3 Case III: Ties Between Both Samples; 8.10 Conclusions; 9 Control Chart Constants for Non-normal Sampling ; 9.1 Introduction; 9.2 Constants d2, d3; 9.3 Constants c4, c5; 9.3.1 Normal Sampling.
9.3.2 Non-normal Sampling9.4 Conclusions; 10 Linear Approximations of Probability DensityFunctions; 10.1 Approximating a PDF; 10.2 Methods for Endpoint Placement; 10.2.1 Equal Spacing; 10.2.2 Placement by Percentiles; 10.2.3 Curvature-Based Approach; 10.2.4 Optimization-Based Approach; 10.3 Comparison of the Methods; 10.4 Application; 10.4.1 Convolution Theorem; 10.4.2 Monte Carlo Approximation; 10.4.3 Convolution of Approximate PDFs; 10.5 Conclusions; 11 Univariate Probability Distributions ; 11.1 Introduction; 11.2 Discussion of Properties; 11.3 Discussion of Relationships.
3.2 P-Vector3.3 Computation of the P-Vector ; 3.4 Goodness-of-Fit Testing; 3.5 Power Estimates for Test Statistics; 3.6 Further Research; 4 The ``Straightforward'' Nature of Arrival Rate Estimation?; 4.1 Introduction; 4.1.1 Sampling Plan 1: Time Sampling; 4.1.2 Sampling Plan 2: Count Sampling; 4.1.3 Sampling Plan 3: Limit Both Time and Arrivals; 4.2 Conclusions; 5 Survival Distributions Based on the Incomplete Gamma Function Ratio ; 5.1 Introduction; 5.2 Properties and Results; 5.3 Examples; 5.4 Conclusions.
6 An Inference Methodology for Life Tests with Full Samples or Type II Right Censoring 6.1 Introduction and Literature Review; 6.2 The Methodology for Censored Data; 6.3 The Uniformity Test Statistic; 6.4 Implementation Using APPL; 6.5 Power Simulation Results; 6.6 Some Applications and Implications; 6.7 Conclusions and Further Research; 7 Maximum Likelihood Estimation Using Probability Density Functions of Order Statistics ; 7.1 Introduction; 7.2 MLEOS with Complete Samples; 7.3 Applying MLEOS to Censored Samples; 7.4 Conclusions and Further Research; 8 Notes on Rank Statistics.
8.1 Introduction8.2 Explanation of the Tests; 8.3 Distribution of the Test Statistic Under H0; 8.4 Wilcoxon Power Curves for n = 2; 8.5 Generalization to Larger Sample Sizes; 8.6 Comparisons and Analysis; 8.7 The Wilcoxon-Mann-Whitney Test; 8.8 Explanation of the Test; 8.9 Three Cases of the Distribution of W Under H0; 8.9.1 Case I: No Ties; 8.9.2 Case II: Ties Only Within Each Sample; 8.9.3 Case III: Ties Between Both Samples; 8.10 Conclusions; 9 Control Chart Constants for Non-normal Sampling ; 9.1 Introduction; 9.2 Constants d2, d3; 9.3 Constants c4, c5; 9.3.1 Normal Sampling.
9.3.2 Non-normal Sampling9.4 Conclusions; 10 Linear Approximations of Probability DensityFunctions; 10.1 Approximating a PDF; 10.2 Methods for Endpoint Placement; 10.2.1 Equal Spacing; 10.2.2 Placement by Percentiles; 10.2.3 Curvature-Based Approach; 10.2.4 Optimization-Based Approach; 10.3 Comparison of the Methods; 10.4 Application; 10.4.1 Convolution Theorem; 10.4.2 Monte Carlo Approximation; 10.4.3 Convolution of Approximate PDFs; 10.5 Conclusions; 11 Univariate Probability Distributions ; 11.1 Introduction; 11.2 Discussion of Properties; 11.3 Discussion of Relationships.