Exponential Distribution: Theory and Methods (Mathematics Research Developments)

EXPONENTIAL DISTRIBUTION:THEORY AND METHODS......Page 3
MATHEMATICS RESEARCH DEVELOPMENTS......Page 4
Contents......Page 9
Preface......Page 11
About the Authors......Page 13
Introduction......Page 15
1.1. Preliminaries......Page 17
2.1. Preliminaries and Definitions......Page 25
2.2. Minimum Variance Linear Unbiased EstimatorsBased on Order Statistics......Page 32
2.3. Minimum Variance Linear Unbiased Predictors(MVLUPs)......Page 38
2.4. Limiting Distributions......Page 41
3.2. The Exact Distribution of Record Values......Page 45
3.3. Moments of Record Values......Page 52
(a) Minimum Variance Linear Unbiased Estimator (MVLUE)......Page 58
(b) Best Linear Invariant Estimator (BLIE)......Page 59
3.5. Prediction of Record Values......Page 60
3.6. Limiting Distribution of Record Values......Page 62
4.1. Definition......Page 65
4.2. Generalized Order Statistics of Exponential Distribution......Page 66
Minimum Variance Linear Unbiased Estimators (MVLUEs)......Page 71
Best Linear Invariant Estimators (BLIEs)......Page 74
Prediction of X (s,n,m, k)......Page 75
5.1. Introduction......Page 79
5.2. Characterizations Based on Order Statistics......Page 80
5.3. Characterizations Based on Generalized Order Statistics......Page 100
6.1. Characterizations Based on Record Values......Page 113
6.2. Characterizations Based on Generalized Order Statistics......Page 134
References......Page 135
Index......Page 157