Hardbound. Volume 17 of the Handbook of Statistics is the concluding volume covering Order Statistics. Dealing primarily with Applications, it is divided into six parts as follows: Results for Specific Distributions, Linear Estimation, Inferential Methods, Prediction, Goodness-of-fit Tests and Applications. Major theoretical advances were made in this area of research, and in the course of these developments order statistics has also found important applications in many diverse areas. These include life-testing and reliability, robustness studies, statistical quality control, filtering theory, signal processing, image processing, and radar target detection.
Theoretical researchers working on theoretical and methodological advancements on order statistics and applied statisticians and engineers developing new and innovative applications of order statistics have been successfully brought together to create this handbook. For the convenience of readers, th
Author(s): N. Balakrishnan, C.R. Rao
Series: North-Holland Mathematical Library 17
Edition: 1
Publisher: Elsevier Science Pub Co
Year: 1998
Language: English
Pages: 733
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
Front cover......Page 1
Series......Page 4
Title page......Page 5
Date-line......Page 6
Preface......Page 7
Table of contents......Page 11
Contributors......Page 19
PART I. RESULTS FOR SPECIFIC DISTRIBUTIONS......Page 21
2. Order statistics and its properties......Page 23
3. Censored data......Page 25
4. Inference concerning several exponential populations......Page 31
5. Order restricted inference......Page 34
6. Bayesian inference......Page 40
References......Page 42
1. Introduction......Page 45
2. Relations for single moments......Page 46
3. Relations for double moments......Page 48
4. Relations for triple moments......Page 51
5. Relations for quadruple moments......Page 56
6. Applications to inference for the one-parameter exponential distribution......Page 63
7. Generalized results for the right-truncated exponential distribution......Page 65
8. Illustrative examples......Page 75
References......Page 78
1. Introduction......Page 81
2. Single moments of order statistics......Page 83
3. Product moments of order statistics......Page 92
4. Best linear unbiased estimators......Page 96
5. Illustrative example......Page 99
References......Page 102
1. Introduction......Page 105
2. Recurrence relations for single moments......Page 108
3. Recurrence relations for product moments......Page 111
4. Recursive computational algorithm......Page 123
5. Best linear unbiased estimators......Page 124
6. Maximum likelihood estimation......Page 125
7. Numerical example......Page 128
8. Introduction......Page 136
9. Recurrence relations for single moments......Page 137
10. Recurrence relations for product moments......Page 139
References......Page 145
1. Introduction......Page 147
2. Type III generalized logistic distribution......Page 148
3. Order statistics and moments......Page 152
4. BLUEs of location and scale parameters......Page 163
5. MLEs of location and scale parameters......Page 167
6. Comparison of the BLUEs with the MLEs......Page 169
7. Illustrative examples......Page 170
References......Page 174
PART II. LINEAR ESTIMATION......Page 177
1. Introduction......Page 179
2. Linear estimators......Page 181
3. The positivity of the best unbiased $L$-estimator......Page 185
4. Nonlinear estimators......Page 186
5. Extension of the positivity results to censored scale regression model......Page 197
6. Concluding remarks......Page 199
References......Page 200
1. Introduction......Page 203
2. Preliminaries......Page 204
3. Optimality criteria for estimation......Page 209
4. Specific distributions......Page 213
5. Tests of significance......Page 223
6. Testing goodness-of-fit......Page 225
References......Page 227
1. Introduction......Page 235
2. Introductory examples......Page 236
3. Single-sample problems......Page 240
4. More complicated problems......Page 250
References......Page 253
1. Introduction......Page 257
2. Regression quantiles and their properties......Page 258
3. $L$-estimation of the parameters of a linear model based on a few selected regression quantiles with known error distributions......Page 261
4. Trimmed least-squared estimation of regression parameters and its asymptotic distribution......Page 271
5. Trimmed estimation of regression parameters under uncertain prior information 271 Acknowledgement......Page 298
References......Page 299
PART III. INFERENTIAL METHODS......Page 301
1. Introduction......Page 303
2. The exponential distribution......Page 304
3. The Weibull distribution......Page 306
4. The lognormal distribution......Page 308
5. The gamma distribution......Page 312
6. The Inverse Gaussian distribution......Page 317
7. Errors of estimates......Page 320
8. Illustrative examples......Page 328
References......Page 332
2. Best linear estimation......Page 335
3. Maximum likelihood estimation......Page 339
4. Approximate maximum likelihood estimation......Page 343
5. Interval estimation for exponential distribution......Page 346
References......Page 353
1. Introduction......Page 357
2. Estimation of a normal mean and a normal variance......Page 361
3. Estimation of an exponential mean......Page 367
4. Estimation of parameters in a two parameter exponential distribution......Page 371
5. Estimation of the location parameter of a Cauchy distribution......Page 378
6. Estimation of location and scale parameters of a logistic distribution......Page 384
7. Estimation of parameters in Weibull and extreme-value distributions......Page 390
References......Page 395
2. Discordancy testing......Page 399
3. Suspicious circumstances......Page 400
4. Examples......Page 401
5. Ransacked data......Page 406
6. Conditional predictive discordancy (CPD) tests......Page 409
7. Combinations of largest and smallest......Page 412
8. Ordering future values......Page 415
9. Multivariate problems......Page 418
References......Page 419
1. Introduction......Page 421
2. The proposed inverse sampling procedures......Page 422
3. Critical values, power and expected sample size......Page 423
4. Comparison with the standard $\chi^2$-test......Page 429
5. The combined procedure......Page 432
References......Page 446
PART IV. PREDICTION......Page 449
1. Introduction......Page 451
2. Prediction preliminaries......Page 452
3. Assumptions and notation......Page 453
4. Point prediction......Page 454
5. Interval prediction......Page 460
References......Page 468
PART V. GOODNESS-OF-FIT TESTS......Page 471
1. Introduction......Page 473
2. Distribution theory for the correlation coefficient......Page 477
3. Tests for the normal distribution......Page 480
4. Tests for the uniform distribution......Page 484
5. Power of correlation tests......Page 487
A. Appendix......Page 488
References......Page 492
1. Introduction......Page 495
2. Probability plotting......Page 496
3. Regression type tests......Page 500
4. Use of spacings of the order statistics......Page 508
References......Page 512
PART VI. APPLICATIONS......Page 515
1. Introduction......Page 517
2. Sampling plans for inspection by variables......Page 518
3. Robustness of variable sampling plans for normal distributed characteristics......Page 519
4. Failure censored sampling plans......Page 520
5. Reduction of test times for life-test sampling plans......Page 526
References......Page 529
1. Introduction......Page 533
2. Models and basic results......Page 534
3. Correlations and linear regressions......Page 535
4. Maximum likelihood and large-sample estimates......Page 538
5. An exact test for $\gamma = 0$......Page 539
6. Numerical examples......Page 540
References......Page 544
1. Introduction......Page 545
2. The estimators......Page 547
3. $\alpha$-trimmed $L^j l$ filters......Page 555
4. Optimization......Page 556
5. Filter lattice structures......Page 560
6. Piecewise linear structure of $L^j l$ filters......Page 562
7. Applications......Page 564
References......Page 573
1. Introduction......Page 575
2. The median filter......Page 579
3. Weighted median filters......Page 590
4. Time-Rank coupling extensions: PWOS filters......Page 600
5. Optimization techniques......Page 611
6. Applications to image restoration......Page 618
7. Conclusion......Page 621
References......Page 622
1. Introduction......Page 623
2. Order statistic filters......Page 625
3. Spatial/temporal extensions......Page 646
4. Morphological filters......Page 648
5. Related OS applications......Page 655
6. Conclusions 638 References......Page 658
1. Introduction......Page 663
2. Order statistics based CFAR tests for Rayleigh clutter......Page 667
3. Order statistics based tests for non-Rayleigh clutter......Page 681
4. Conclusion......Page 688
References......Page 689
Author Index......Page 693
Subject Index......Page 699
Contents of Previous Volumes......Page 715
Back cover......Page 733
