Relations, Bounds and Approximations for Order Statistics
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1: The Distribution of Order Statistics.- Exercises.- 2: Recurrence Relations and Identities for Order Statistics.- 2.0. Introduction.- 2.1. Relations for single moments.- 2.2. Relations for product moments.- 2.3. Relations for covariances.- 2.4. Results for symmetric populations.- 2.5. Results for normal population.- 2.6. Results for two related populations.- 2.7. Results for exchangeable variates.- Exercises.- 3: Bounds on Expectations of Order Statistics.- 3.0. Introduction.- 3.1. Universal bounds in the i.i.d. case.- 3.2. Variations on the Samuelson-Scott theme.- 3.3. Bounds via maximal dependence.- 3.4. Restricted families of parent distributions.- Exercises.- 4: Approximations to Moments of Order Statistics.- 4.0. Introduction.- 4.1. Uniform order statistics and moments.- 4.2. David and Johnson's approximation.- 4.3. Clark and Williams' approximation.- 4.4. Plackett's approximation.- 4.5. Saw's error analysis.- 4.6. Sugiura's orthogonal inverse expansion.- 4.7. Joshi's modified bounds and approximations.- 4.8. Joshi and Balakrishnan's improved bounds for extremes.- Exercises.- 5: Order Statistics From a Sample Containing a Single Outlier.- 5.0. Introduction.- 5.1. Distributions of order statistics.- 5.2. Relations for single moments.- 5.3. Relations for product moments.- 5.4. Relations for covariances.- 5.5. Results for symmetric outlier model.- 5.6 Results for two related outlier models.- 5.7. Functional behaviour of order statistics.- 5.8. Applications in robustness studies.- Exercises.- 6: Record Values.- 6.0. Introduction.- 6.1. Record values.- 6.2. Bounds on mean record values.- 6.3. Record values in dependent sequences.- Exercises.- References.- Author Index.