Record Values Theory and Applications

In this book, Mohammad Ahsanullah provides a detailed description of the general theory and applications of record values. Professor Ahsanullah thoroughly discusses the most useful distributions and inferences based on record values, resulting in conclusions that are not available in previously published works.

Mohammad Ahsanullah is Professor in the Department of Management Sciences at Rider University in Lawrenceville, New Jersey.

Preface

vii

Abbreviations

viii

Record Statistics

Introduction and Examples of Record Values

1

(1)

Definition of Record Values and Record Times

2

(1)

The Exact Distribution of Record Values

2

(6)

Moments of Record Values

8

(17)

Distribution of Inter-Record Times

25

(12)

Relation Between Occurrences of Records and Poisson Processes

37

(2)

Number of Records In A Sequence of Observations

39

(3)

Distribution of Inter-Record Times

42

(1)

The K-Records

43

(17)

Entropies of Record Values

60

(3)

Exponential Distribution

Introduction

63

(1)

Distribution of Record Values

64

(2)

Moments of Record Values

66

(8)

Estimation of Parameters

74

(4)

Characterizations

78

(18)

Prediction of Record values

96

(2)

Limiting Distributions of Record Values

98

(3)

Generalized Extreme Value Distribution

Introduction

101

(3)

Distributional Properties

104

(2)

Recurrence Relations Between Moments

106

(6)

Estimation of Parameters

112

(10)

Prediction of Record Values

122

(1)

Characterizations

123

(2)

Applications

125

(4)

Limiting Distributions

129

(2)

Generalized Pareto Distribution

Introduction

131

(1)

Distributional Properties

132

(2)

Recurrence Relations of Moments

134

(8)

Estimation of Parameters

142

(4)

Prediction of Record Values

146

Classical Pareto Distribution

137

(13)

Lomax Distribution

150

(5)

Power Function Distribution

Introduction

155

(1)

Distributional Properties

156

(2)

Recurrence Relations Between Moments

158

(7)

Estimation of Parameters

165

(4)

Prediction of Record Values

169

(2)

One Parameter Uniform Distribution

171

(6)

Discrete Distribution

Introduction

177

(4)

Geometric Distribution

181

(11)

Records of Non-Identically Distributed Random Variables

192

(3)

Weak Records

195

(14)

Some Selected Distributions

Introduction

209

(1)

Logistic Distribution

209

(6)

Normal Distribution

215

(3)

Rayleigh Distribution

218

(6)

Two Parameter Uniform Distribution

224

(9)

Weibull Distribution

233

(7)

Distributions Where Consecutive Record Values Have Linear Regression

240

(9)

Additional Topics

Introduction

249

(1)

Limiting Distribution of Inter-Record times

249

(3)

Limiting Distribution of Record Values

252

(2)

Limiting Distribution of Record Times

254

(2)

Representation of Records

256

(2)

Limiting Distribution of Number of Records

258

(3)

Random Record Model

261

(6)

Records of Dependent Sequence

267

(2)

Concomitants

269

(6)

APPENDIX

A.1 Stirling Numbers of the First Kind

275

(1)

A.2 Bernoulli Numbers

276

(1)

A.3 Cauchy Type Functional Equation

277

(4)

Complements and Problems

281

(12)

References

293

(22)

Index

315

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Record Values Theory and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials

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Record Values Theory and Applications

Summary

Author Biography

Table of Contents

Supplemental Materials

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