Relations Bounds and Approximations for Order Statistics

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. Language: English