Stochastic Orders (Springer Series in Statistics)

Preface......Page 7
Contents......Page 11
Note......Page 17
1.A The Usual Stochastic Order......Page 19
1.B The Hazard Rate Order......Page 32
1.C The Likelihood Ratio Order......Page 58
1.D The Convolution Order......Page 86
1.E Complements......Page 87
2.A The Mean Residual Life Order......Page 97
2.B The Harmonic Mean Residual Life Order......Page 110
2.C Complements......Page 122
3.A The Convex Order......Page 125
3.B The Dispersive Order......Page 162
3.C The Excess Wealth Order......Page 179
3.D The Peakedness Order......Page 187
3.E Complements......Page 190
4.A The Monotone Convex and Monotone Concave Orders......Page 197
4.B Transform Orders: The Convex, Star, and Superadditive Orders......Page 229
4.C Complements......Page 243
5.A The Laplace Transform Order......Page 249
5.B Orders Based on Ratios of Laplace Transforms......Page 261
5.C Some Related Orders......Page 268
5.D Complements......Page 277
6.A Notations and Preliminaries......Page 281
6.B The Usual Multivariate Stochastic Order......Page 282
6.C The Cumulative Hazard Order......Page 302
6.D Multivariate Hazard Rate Orders......Page 306
6.E The Multivariate Likelihood Ratio Order......Page 314
6.F The Multivariate Mean Residual Life Order......Page 321
6.G Other Multivariate Stochastic Orders......Page 323
6.H Complements......Page 333
7.A The Monotone Convex and Monotone Concave Orders......Page 339
7.B Multivariate Dispersion Orders......Page 358
7.C Multivariate Transform Orders: Convex, Star, and Superadditive Orders......Page 364
7.D The Multivariate Laplace Transform and Related Orders......Page 365
7.E Complements......Page 370
8.A Regular Stochastic Convexity......Page 373
8.B Sample Path Convexity......Page 383
8.C Convexity in the Usual Stochastic Order......Page 390
8.D Strong Stochastic Convexity......Page 393
8.E Stochastic Directional Convexity......Page 397
8.F Complements......Page 400
9.A The PQD and the Supermodular Orders......Page 403
9.B The Orthant Ratio Orders......Page 420
9.C The LTD, RTI, and PRD Orders......Page 424
9.D The PLRD Order......Page 430
9.E Association Orders......Page 433
9.F The PDD Order......Page 436
9.G Ordering Exchangeable Distributions......Page 439
9.H Complements......Page 442
References......Page 447
Author Index......Page 475
Subject Index......Page 483