Hybrid Censoring Know-How: Models, Methods and Applications focuses on hybrid censoring, an important topic in censoring methodology with numerous applications. The readers will find information on the significance of censored data in theoretical and applied contexts, and descriptions of extensive data sets from life-testing experiments where these forms of data naturally occur. The existing literature on censoring methodology, life-testing procedures, and lifetime data analysis provides only hybrid censoring schemes, with little information about hybrid censoring methodologies, ideas, and statistical inferential methods. This book fills that gap, featuring statistical tools applicable to data from medicine, biology, public health, epidemiology, engineering, economics, and demography.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Preliminaries - p. 19 3. Abstract - p. 19 4. Contents - p. page19 5. 2.1 Introduction - p. page19 6. 2.2 Order statistics - p. 20 7. 2.3 Progressively Type-II right censored order statistics - p. 42 8. 2.4 Generalized order statistics - p. page57 9. 2.5 Sequential order statistics - p. page58 10. Bibliography - p. 59 11. Chapter 3. Inference for Type-II, Type-I, and progressive censoring - p. 61 12. Abstract - p. 61 13. Contents - p. page61 14. 3.1 Introduction - p. page61 15. 3.2 Type-II censoring - p. page61 16. 3.3 Type-I censoring - p. 103 17. 3.4 Progressive Type-II censoring - p. 109 18. 3.5 Progressive Type-I censoring - p. 116 19. Bibliography - p. 118 20. Chapter 4. Models and distributional properties of hybrid censoring designs - p. 119 21. Abstract - p. 119 22. Contents - p. page119 23. 4.1 Introduction - p. page119 24. 4.2 Preliminaries - p. 120 25. 4.3 Type-I hybrid censoring - p. 124 26. 4.4 Type-II hybrid censoring - p. 135 27. 4.5 Further hybrid censoring schemes - p. page140 28. 4.6 Joint (hybrid) censoring - p. 152 29. Bibliography - p. 153 30. Chapter 5. Inference for exponentially distributed lifetimes - p. 155 31. Abstract - p. 155 32. Contents - p. page155 33. 5.1 Introduction - p. page155 34. 5.2 General expression for the likelihood function - p. 157 35. 5.3 Type-I hybrid censoring - p. 156 36. 5.4 Type-II hybrid censoring - p. 176 37. 5.5 Further hybrid censoring schemes - p. 184 38. Bibliography - p. 188 39. Chapter 6. Inference for other lifetime distributions - p. 189 40. Chapter 7. Progressive hybrid censored data - p. 207 41. Abstract - p. 207 42. Contents - p. page207 43. 7.1 Progressive (hybrid) censoring schemes - p. page207 44. 7.2 Exponential case: MLEs and its distribution - p. 219 45. 7.3 Progressive hybrid censored data: other cases - p. 246 46. Bibliography - p. 250 47. Chapter 8. Information measures - p. 251 48. Abstract - p. 251 49. Contents - p. page251 50. 8.1 Introduction - p. page251 51. 8.2 Fisher information - p. page251 52. 8.3 Entropy - p. 273 53. 8.4 Kullback-Leibler information - p. 278 54. 8.5 Pitman closeness - p. 277 55. Bibliography - p. 279 56. Chapter 9. Step-stress testing - p. 281 57. Chapter 10. Applications in reliability - p. 297 58. Abstract - p. 297 59. Contents - p. page297 60. 10.1 Introduction - p. page297 61. 10.2 Competing risks analysis - p. page297 62. 10.3 Stress-strength models - p. 309 63. 10.4 Optimal designs - p. 310 64. 10.5 Reliability acceptance sampling plans - p. 314 65. Bibliography - p. 319 66. Chapter 11. Goodness-of-fit tests - p. 321 67. Chapter 12. Prediction methods - p. 331 68. Chapter 13. Adaptive progressive hybrid censoring - p. 345 69. Appendix - p. 353 70. Bibliography - p. 361 71. Index - p. 387
Hybrid Censoring Know-How: Models, Methods and Applications focuses on hybrid censoring, an important topic in censoring methodology with numerous applications. The readers will find information on the significance of censored data in theoretical and applied contexts, and descriptions of extensive data sets from life-testing experiments where these forms of data naturally occur. The existing literature on censoring methodology, life-testing procedures, and lifetime data analysis provides only hybrid censoring schemes, with little information about hybrid censoring methodologies, ideas, and statistical inferential methods. This book fills that gap, featuring statistical tools applicable to data from medicine, biology, public health, epidemiology, engineering, economics, and demography.
1. Chapter 1. Introduction - p. 1 2. Chapter 2. Preliminaries - p. 19 3. Abstract - p. 19 4. Contents - p. page19 5. 2.1 Introduction - p. page19 6. 2.2 Order statistics - p. 20 7. 2.3 Progressively Type-II right censored order statistics - p. 42 8. 2.4 Generalized order statistics - p. page57 9. 2.5 Sequential order statistics - p. page58 10. Bibliography - p. 59 11. Chapter 3. Inference for Type-II, Type-I, and progressive censoring - p. 61 12. Abstract - p. 61 13. Contents - p. page61 14. 3.1 Introduction - p. page61 15. 3.2 Type-II censoring - p. page61 16. 3.3 Type-I censoring - p. 103 17. 3.4 Progressive Type-II censoring - p. 109 18. 3.5 Progressive Type-I censoring - p. 116 19. Bibliography - p. 118 20. Chapter 4. Models and distributional properties of hybrid censoring designs - p. 119 21. Abstract - p. 119 22. Contents - p. page119 23. 4.1 Introduction - p. page119 24. 4.2 Preliminaries - p. 120 25. 4.3 Type-I hybrid censoring - p. 124 26. 4.4 Type-II hybrid censoring - p. 135 27. 4.5 Further hybrid censoring schemes - p. page140 28. 4.6 Joint (hybrid) censoring - p. 152 29. Bibliography - p. 153 30. Chapter 5. Inference for exponentially distributed lifetimes - p. 155 31. Abstract - p. 155 32. Contents - p. page155 33. 5.1 Introduction - p. page155 34. 5.2 General expression for the likelihood function - p. 157 35. 5.3 Type-I hybrid censoring - p. 156 36. 5.4 Type-II hybrid censoring - p. 176 37. 5.5 Further hybrid censoring schemes - p. 184 38. Bibliography - p. 188 39. Chapter 6. Inference for other lifetime distributions - p. 189 40. Chapter 7. Progressive hybrid censored data - p. 207 41. Abstract - p. 207 42. Contents - p. page207 43. 7.1 Progressive (hybrid) censoring schemes - p. page207 44. 7.2 Exponential case: MLEs and its distribution - p. 219 45. 7.3 Progressive hybrid censored data: other cases - p. 246 46. Bibliography - p. 250 47. Chapter 8. Information measures - p. 251 48. Abstract - p. 251 49. Contents - p. page251 50. 8.1 Introduction - p. page251 51. 8.2 Fisher information - p. page251 52. 8.3 Entropy - p. 273 53. 8.4 Kullback-Leibler information - p. 278 54. 8.5 Pitman closeness - p. 277 55. Bibliography - p. 279 56. Chapter 9. Step-stress testing - p. 281 57. Chapter 10. Applications in reliability - p. 297 58. Abstract - p. 297 59. Contents - p. page297 60. 10.1 Introduction - p. page297 61. 10.2 Competing risks analysis - p. page297 62. 10.3 Stress-strength models - p. 309 63. 10.4 Optimal designs - p. 310 64. 10.5 Reliability acceptance sampling plans - p. 314 65. Bibliography - p. 319 66. Chapter 11. Goodness-of-fit tests - p. 321 67. Chapter 12. Prediction methods - p. 331 68. Chapter 13. Adaptive progressive hybrid censoring - p. 345 69. Appendix - p. 353 70. Bibliography - p. 361 71. Index - p. 387
