Author | Arnold, Barry C. author |
---|---|
Title | Relations, Bounds and Approximations for Order Statistics [electronic resource] / by Barry C. Arnold, Narayanaswamy Balakrishnan |
Imprint | New York, NY : Springer New York, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3644-3 |
Descript | IX, 173 p. online resource |
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 Johnsonโs approximation -- 4.3. Clark and Williamsโ approximation -- 4.4. Plackettโs approximation -- 4.5. Sawโs error analysis -- 4.6. Sugiuraโs orthogonal inverse expansion -- 4.7. Joshiโs modified bounds and approximations -- 4.8. Joshi and Balakrishnanโs 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