The exponential distribution: theory, methods and applications
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Amsterdam
Gordon and Breach
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 638 S. graph. Darst. |
| ISBN: | 2884491929 |
Staff View
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Record in the Search Index
| _version_ | 1804125748668137472 |
|---|---|
| adam_text | Contents
List of Tables xvii
List of Figures xix
Preface xxi
List of Contributors xxiii
1. Genesis
Norman L. Johnson, Samuel Kotz, and N. Balakrishnan 1
1.1 Preliminaries 1
1.2 Historical Remarks 2
References 4
2. Basic Distributional Results and Properties
Asit P. Basu and Nader Ebrahimi 7
2.1 Introduction 7
2.2 Basic Results and Properties 8
References 14
3. Order Statistics and Their Properties
N. Balakrishnan and Bimal K. Sinha 17
3.1 Introduction 17
3.2 Basic Distributional Results and Properties 18
3.3 Recurrence Relations 19
3.4 Lorenz Ordering 20
3.5 Asymptotic Distributions 21
3.6 Relationship to Uniform Order Statistics 22
3.7 Relationship to Geometric Order Statistics 23
3.8 Relationship to Double Exponential Order Statistics 23
3.9 Results for a Progressive Type II Censored Sample 25
3.10 Results for Right Truncated Exponential Distribution 26
3.11 Results for Doubly Truncated Exponential Distribution 28
References 29
viii Contents
4. MLEs Under Censoring and Truncation and Inference
A. Clifford Cohen 33
4.1 Introduction 33
4.2 Parameter Estimation from Censored Samples 35
4.3 Estimation in Truncated Distributions 38
4.4 Errors of Estimates 41
4.5 Illustrative Examples 42
References 49
5. Linear Estimation Under Censoring and Inference
N. Balakrishnan and R.A. Sandhu 53
5.1 Introduction 53
5.2 Type II Right Censored Samples 53
5.3 Type II Doubly Censored Samples 56
5.4 Type II Multiply Censored Samples 58
5.5 Type II Progressively Right Censored Samples 60
5.6 General Type II Progressively Censored Samples 61
5.7 Asymptotic Best Linear Unbiased Estimation Based On
Optimally Selected Order Statistics 64
5.8 Illustrative Examples 66
References 70
6. Reliability Estimation and Applications
Max Engelhardt 73
6.1 Introduction 73
6.2 Estimation with the One Parameter Model 74
6.3 Estimation with the Two Parameter Model 83
References 90
7. Inferences Under Two Sample and Multi Sample Situations
Gouri K. Bhattacharyya 93
7.1 Introduction 93
7.2 Notation and Preliminaries 95
7.3 Two Sample Inferences Under Independent Type II
Censoring 97
7.4 Comparison of Several Populations Under Independent
Type II Censoring 103
7.5 Two Sample Inferences Under Joint Type II Censoring 110
7.6 Miscellaneous Other Results 114
References 116
Contents ix
8. Tolerance Limits and Acceptance Sampling Plans
Lam Yeh and N. Balakrishnan 119
8.1 Introduction 119
8.2 One Sided Tolerance Limits 120
8.3 One and Two Sided Sampling Plans 125
8.4 Bayesian Sampling Plans 128
References 136
9. Prediction Problems
H.N. Nagaraja 139
9.1 Introduction 139
9.2 Types of Prediction Problems 141
9.3 Best Linear Unbiased and Invariant Predictors 142
9.4 Maximum Likelihood Prediction 144
9.5 Prediction Intervals and Regions 145
9.6 Bayes Predictors and Prediction Regions 153
9.7 Other Prediction Methods 154
9.8 Miscellaneous Results 156
9.9 Concluding Remarks 157
References 157
10. Bayesian Inference and Applications
Asit P. Basu 165
10.1 Introduction 165
10.2 Bayesian Concepts 166
10.3 Life Testing and Reliability Estimation 167
10.4 Bayesian Classification Rules 168
References 170
11. Conditional Inference and Applications
Roman Viveros 173
11.1 Ancillarity and Conditionality: A Brief Overview 173
11.2 A Simple Example 174
11.3 One Parameter Exponential Model 175
11.4 Exponential Regression 178
11.5 Discussion 181
References 181
12. Characterizations
Barry C. Arnold and J.S. Huang 185
12.1 Let Me Count the Ways 185
12.2 Lack of Memory 186
12.3 Distributional Relations Among Order Statistics 187
x Contents
12.4 Independence of Functions of Order Statistics 190
12.5 Moments of Order Statistics 191
12.6 Characterizations Involving Geometric Compounding 193
12.7 Record Value Concepts 196
12.8 Miscellaneous Characterizations 198
References 199
13. Goodness of Fit Tests
Samuel S. Shapiro 205
13.1 Introduction 205
13.2 Graphical Procedures 206
13.3 Regression Tests 208
13.4 Spacing Tests 210
13.5 EDF Tests 213
13.6 Tests Based on a Characterization 214
13.7 Power Comparisons 214
13.8 Examples of Calculations 215
13.9 Summary 218
References 218
14. Outliers and Some Related Inferential Issues
U. Gather 221
14.1 Introduction 221
14.2 Outlier Generating Models 222
14.3 Outlier Tests Testing for Contamination 227
14.4 Identification of Outliers 232
14.5 Estimation of the Scale Parameters of an Exponential
Distribution in Outlier Situations 233
References 235
15. Extensions to Estimation Under Multiple Outlier Models
N. Balakrishnan and A. Chilis 241
15.1 Introduction 241
15.2 The Recurrence Relations 242
15.3 The Estimators 245
15.4 Optimal Estimators of 6 Under the
Multiple Outlier Model 247
15.5 Efficient Estimation of 9 Under the
Multiple Outlier Model 247
15.6 Examples 248
15.7 Extensions to the Double Exponential Model 249
References 250
Contents xi
16. Selection and Ranking Procedures
S. Panchapakesan 259
16.1 Introduction 259
16.2 Selection and Ranking Formulations 259
16.3 Selection from One Parameter (Scale) Exponential
Populations 261
16.4 Selection from Two Parameter (Location and Scale)
Exponential Populations 264
16.5 Selection with Respect to a Standard or Control 271
16.6 Estimation Concerning Selected Populations 273
16.7 Concluding Remarks 274
References 275
17. Record Values
M. Ahsanullah 279
17.1 Introduction 279
17.2 Distribution of Record Values 280
17.3 Moments of Record Values 282
17.4 Inter Record Times 286
17.5 Linear Estimation of Location and Scale Parameters 289
17.6 Prediction of Record Values 291
17.7 5 Exceedance Records 292
References 294
18. Related Distributions and Some Generalizations
Norman L. Johnson, Samuel Kotz, and N. Balakrishnan 297
18.1 Introduction 197
18.2 Transformed Distributions 297
18.3 Quadratic Forms 298
18.4 Mixtures of Exponential Distributions 299
18.5 Gamma Distributions 301
18.6 Linear Exponential Distributions 301
18.7 Wear Out Life Distributions 302
18.8 Ryu s Generalized Exponential Distributions 303
18.9 Brittle Fracture Distributions 303
18.10 Geometric and Poisson Distributions 303
References 304
19. Mixtures Models and Applications
G.J. McLachlan 307
19.1 Introduction 307
19.2 Maximum Likelihood Estimation 308
19.3 Partially Classified Data 312
19.4 Testing for the Number of Components 313
xii Contents
19.5 Provision of Standard Errors 314
19.6 Homogeneity of Mixing Proportions 316
19.7 Generalized Mixtures of Exponentials 317
19.8 Some Further Extensions 318
19.9 Example 318
References 320
20. Bivariate Exponential Distributions
Asit P. Basu 327
20.1 Introduction 327
20.2 Gumbel s Distributions 328
20.3 Freund s Model 329
20.4 Marshall Olkin Model 329
20.5 Block Basu Model 330
20.6 Other Distributions 331
References 331
21. Inference for Multivariate Exponential Distributions
John P. Klein 333
21.1 Introduction 333
21.2 Inference for the Marshall Olkin Model 333
21.3 Inference for the Freund Model 337
21.4 Inference for the Block Basu Model 340
21.5 Inference for Exponential Frailty Models 343
21.6 Inference for Other Multivariate Exponential Models 346
References 347
22. Optimal Tests in Multivariate Exponential Distributions
Ashis SenGupta 351
22.1 Introduction and Summary 351
22.2 Independent Exponentials 352
22.3 Marshall Olkin (MO) Model 352
22.4 Marshall Olkin Hyakutake (MOH) Model 356
22.5 Multivariate Marshall Olkin (M MO) Model 357
22.6 Block Basu (BB) Model 358
22.7 A Trivariate Block Basu (T BB) Model 361
22.8 Multivariate Block Basu (M BB) Model 362
22.9 Scaled Exponential Dependency Parameter (BK) Models 364
22.10 Gumbel III (GUI) Model 365
22.11 Gumbel III Model Under a Type II Censoring Scheme 366
22.12 Freund (F) Model 367
22.13 Arnold Strauss (AS) Model 369
22.14 Mixture Models 370
22.15 Non Regular Models 371
Contents xijj
22.16 Other Models 372
References 372
23. Accelerated Life Testing with Applications
Asit P. Basu 377
23.1 Introduction 377
23.2 The Models 378
23.3 Estimation for Power Rule Model 378
23.4 Competing Causes of Failure 380
23.5 Bivariate Accelerated Life Tests 382
References 382
24. System Reliability and Associated Inference
S. Zacks 385
24.1 Introduction 385
24.2 System Reliability Functions 387
24.3 Estimating System Reliability 388
24.4 Bootstrapping Estimates 390
24.5 Estimating the Reliability Function of an r out of A;
System: Censored Global Observations 392
24.6 Estimating the Time of Shift into the Wear Out Phase 394
24.7 Determination of Burn In Time 399
References 401
25. Exponential Regression with Applications
Richard A. Johnson and Rick Chappell 403
25.1 Introduction 403
25.2 Censoring 405
25.3 Estimation 406
25.4 Testing 410
25.5 Examples 411
References 416
Appendix 1 425
Appendix 2 428
26. Two Stage and Multi Stage Estimation
N. Mukhopadhyay 429
26.1 Introduction 429
26.2 Fixed Width Confidence Intervals for the Location 431
26.3 Fixed Precision Estimation of a Positive Location 435
26.4 Minimum Risk Point Estimation of the Location 435
26.5 Sequential Point Estimation Procedures for the
Scale Parameter, Mean and Percentiles 438
26.6 Multi Sample Problems 441
xiv Contents
26.7 Combining Sequential and Multi Stage Estimation
Procedures 446
26.8 Time Sequential Methodologies 447
References 448
27. Two Stage and Multi Stage Tests of Hypotheses
J.E. Hewett 453
27.1 Introduction 453
27.2 One Population Problem 455
27.3 Two Population Problem 456
27.4 Tests for Exponentiality . 457
27.5 Distribution Free Tests 459
References 459
28. Sequential Inference
Pranab K. Sen 461
28.1 Introduction 461
28.2 A Sequential Probability Ratio Test 463
28.3 Sequential Life Testing Procedures 466
28.4 Sequential Estimation 469
28.5 Sequential Inference Under Random Censoring 475
28.6 Sequential Comparison of Two Exponential Distributions 478
28.7 Sequential Inference for Systems Availability Parameter 480
28.8 Some General Remarks on Sequential Inference 483
References 486
29. Competing Risks Theory and Identifiability Problems
A. P. Basu and J.K. Ghosh 489
29.1 Introduction 489
29.2 Identifiability 490
29.3 Estimation of Parameters 492
References 494
30. Applications in Survival Analysis
Alan J. Gross 497
30.1 Introduction 497
30.2 Basic Formulation 498
30.3 The Exponential Survival Distribution in the
Presence of Covariables 500
30.4 Planning of Clinical Trials: The Use of the Exponential
to Obtain Sample Size Estimates 502
30.5 Bivariate and Multivariate Exponential Distributions
in Survival Analysis 503
References 505
Contents xv
31. Applications in Queueing Theory
J. George Shanthikumar 509
31.1 Introduction 509
31.2 Some Useful General Principles in
Queueing Theory 511
31.3 Exponential Inputs: Simplified Analysis
and Exponential Outputs 513
31.4 Bounds and Applications: Use of Exponential
Inputs and Outputs 520
References 523
32. Exponential Classification and Applications
N. Balakrishnan, S. Panchapakesan, and Q. Zhang 525
32.1 Introduction 525
32.2 Classification When Parameters Are Known 526
32.3 Classification When Parameters Are Unknown 527
32.4 Classification Under Type II Right Censoring 533
32.5 Classification with Guaranteed Life Time 536
32.6 Classification When Parameters Are Unknown but with
Known Ordering 543
References 545
33. Computer Simulations
Pandu R. Tadikamalla and N. Balakrishnan 547
33.1 Introduction 547
33.2 Simulation 548
33.3 Computer Simulation of Order Statistics 552
33.4 Computer Simulation of Progressive Type II
Censored Samples 554
References 555
Bibliography 559
Author Index 617
Subject Index 629
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| indexdate | 2024-07-09T18:06:30Z |
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| language | English |
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| spelling | The exponential distribution theory, methods and applications ed. by N. Balakrishnan ... Amsterdam Gordon and Breach 1995 XXV, 638 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Familles exponentielles (Statistique) Familles exponentielles (statistique) ram Verdelingen (statistiek) gtt Distribution (Probability theory) Exponential families (Statistics) Exponentialverteilung (DE-588)4016019-1 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd rswk-swf Wahrscheinlichkeitsverteilung (DE-588)4121894-2 s DE-604 Exponentialverteilung (DE-588)4016019-1 s Balakrishnan, Narayanaswamy 1956- Sonstige (DE-588)122214846 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007549033&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The exponential distribution theory, methods and applications Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Familles exponentielles (Statistique) Familles exponentielles (statistique) ram Verdelingen (statistiek) gtt Distribution (Probability theory) Exponential families (Statistics) Exponentialverteilung (DE-588)4016019-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4016019-1 (DE-588)4121894-2 |
| title | The exponential distribution theory, methods and applications |
| title_auth | The exponential distribution theory, methods and applications |
| title_exact_search | The exponential distribution theory, methods and applications |
| title_full | The exponential distribution theory, methods and applications ed. by N. Balakrishnan ... |
| title_fullStr | The exponential distribution theory, methods and applications ed. by N. Balakrishnan ... |
| title_full_unstemmed | The exponential distribution theory, methods and applications ed. by N. Balakrishnan ... |
| title_short | The exponential distribution |
| title_sort | the exponential distribution theory methods and applications |
| title_sub | theory, methods and applications |
| topic | Distribution (Théorie des probabilités) Distribution (théorie des probabilités) ram Familles exponentielles (Statistique) Familles exponentielles (statistique) ram Verdelingen (statistiek) gtt Distribution (Probability theory) Exponential families (Statistics) Exponentialverteilung (DE-588)4016019-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Distribution (Théorie des probabilités) Distribution (théorie des probabilités) Familles exponentielles (Statistique) Familles exponentielles (statistique) Verdelingen (statistiek) Distribution (Probability theory) Exponential families (Statistics) Exponentialverteilung Wahrscheinlichkeitsverteilung |
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