EXPONENTIAL DISTRIBUTION:THEORY AND METHODS

MATHEMATICS RESEARCHDEVELOPMENTS

Contents

Preface

About the Authors

Introduction

1.1. Preliminaries

Order Statistics

2.1. Preliminaries and Definitions

2.2. Minimum Variance Linear Unbiased EstimatorsBased on Order Statistics

2.3. Minimum Variance Linear Unbiased Predictors(MVLUPs)

2.4. Limiting Distributions

Record Values

3.1. Definitions of Record Values and Record Times

3.2. The Exact Distribution of Record Values

3.3. Moments of Record Values

3.4. Estimation of Parameters

(a) Minimum Variance Linear Unbiased Estimator (MVLUE)

(b) Best Linear Invariant Estimator (BLIE)

3.5. Prediction of Record Values

3.6. Limiting Distribution of Record Values

Generalized Order Statistics

4.1. Definition

4.2. Generalized Order Statistics of ExponentialDistribution

Estimation of μ and s

Minimum Variance Linear Unbiased Estimators (MVLUEs)

Best Linear Invariant Estimators (BLIEs)

Prediction of X (s,n,m, k)

Characterizations ofExponential Distribution I

5.1. Introduction

5.2. Characterizations Based on Order Statistics

5.3. Characterizations Based on Generalized OrderStatistics

Characterizations ofExponential Distribution II

6.1. Characterizations Based on Record Values

6.2. Characterizations Based on Generalized OrderStatistics

References

Index