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E-raamat: Hybrid Censoring Know-How: Designs and Implementations

(Distinguished University Professor, Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada), (Rahul and Namita Gautam), (Institute for Statistics and Business Mathematics, RWTH Aachen, Aachen, Germany)
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 06-Jan-2023
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780123983909
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Hybrid Censoring Know-How: Designs and ImplementationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 06-Jan-2023
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780123983909
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This book focuses on hybrid censoring, a specific but important topic in censoring methodology, which has numerous applications. Applied statisticians in many fields must frequently analyze time to event data. The statistical tools presented in this book are applicable to data from medicine, biology, public health, epidemiology, engineering, economics, and demography.

This book presents why the analysis of censored data is important from an applied point of view as well as from a theoretical point of view. Extensive data sets from life-testing experiments where these forms of data occur naturally are described. AThe analysis of survival experiments is complicated by issues of censoring, where an individual's life length is known to occur only in a certain period of time, and by truncation, where individuals enter the study only if they survive a sufficient length of time or individuals are included in the study only if the event has occurred by a given date.

The existing literature on censoring methodology, life-testing procedures or lifetime data analysis provide only some hybrid censoring schemes but do not spend a significant amount of time to detail the methodologies, ideas and statistical inferential methods for hybrid censoring. This book fills this gap and provides valuable information on these topics.

  • Presents many numerical examples to adequately illustrate all the inferential methods discussed
  • Provides open problems and possible directions for future work
  • Reviews developments pertaining to Type-II HCS and includes the most recent research and trends
  • Explains why the hybrid censored sampling is important, provides detail in using HCS under different settings and the designs of HCS
  • Includes R code on website for ease of use


Hybrid Censoring: Models, Methods and Applications for Engineering and Bio Healthfocuses on hybrid censoring, a specific, but important topic in censoring methodology that has numerous applications.

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.

As existing literature on censoring methodology, life-testing procedures, or lifetime data analysis provide only hybrid censoring schemes and little information on the methodologies, ideas, and statistical inferential methods for hybrid censoring, this book fills that gap, giving readers valuable information on these topics.

The statistical tools presented within are applicable to data from medicine, biology, public health, epidemiology, engineering, economics, and demography.

  • Presents many numerical examples to adequately illustrate all the inferential methods discussed
  • Provides open problems and possible directions for future work
  • Reviews developments pertaining to Type-II HCS, and includes the most recent research and trends
  • Explains why the hybrid censored sampling is important
  • Provides detail in using HCS under different settings and the designs of HCS
  • Includes R code on website for ease of use

Arvustused

Life science and engineering scientists and researchers who need to analyze censored or truncated life time data and students, researchers and practitioners in different areas such as statistics, industrial engineering and clinical trials.

Muu info

This comprehensive review of hybrid censoring research includes recent developments in the field with numerous applications for medicine, biology, public health, epidemiology, engineering, economics and demography
Preface xi
1 Introduction
1(18)
1.1 Historical perspectives
1(1)
1.2 Type-I and Type-II censoring
2(2)
1.3 Need for hybrid censoring
4(6)
1.4 Antecedents
10(3)
1.5 Burgeoning literature
13(1)
1.6 Scope of the book
13(2)
1.7 Notation
15(4)
2 Preliminaries
19(42)
2.1 Introduction
19(1)
2.2 Order statistics
20(22)
2.3 Progressively Type-II right censored order statistics
42(15)
2.4 Generalized order statistics
57(1)
2.5 Sequential order statistics
58(3)
3 Inference for Type-II, Type-I, and progressive censoring
61(58)
3.1 Introduction
61(1)
3.2 Type-II censoring
61(42)
3.3 Type-I censoring
103(6)
3.4 Progressive Type-II censoring
109(7)
3.5 Progressive Type-I censoring
116(3)
4 Models and distributional properties of hybrid censoring designs
119(36)
4.1 Introduction
119(1)
4.2 Preliminaries
120(4)
4.3 Type-I hybrid censoring
124(11)
4.4 Type-II hybrid censoring
135(5)
4.5 Further hybrid censoring schemes
140(12)
4.6 Joint (hybrid) censoring
152(3)
5 Inference for exponentially distributed lifetimes
155(34)
5.1 Introduction
155(1)
5.2 General expression for the likelihood function
155(2)
5.3 Type-I hybrid censoring
157(19)
5.4 Type-II hybrid censoring
176(8)
5.5 Further hybrid censoring schemes
184(5)
6 Inference for other lifetime distributions
189(18)
6.1 Introduction
189(1)
6.2 Weibull distributions
189(5)
6.3 Further distributions
194(13)
7 Progressive hybrid censored data
207(44)
7.1 Progressive (hybrid) censoring schemes
207(12)
7.2 Exponential case: MLEs and its distribution
219(27)
7.3 Progressive hybrid censored data: other cases
246(5)
8 Information measures
251(30)
8.1 Introduction
251(1)
8.2 Fisher information
251(22)
8.3 Entropy
273(3)
8.4 Kullback--Leibler information
276(2)
8.5 Pitman closeness
278(3)
9 Step-stress testing
281(16)
9.1 Introduction
281(2)
9.2 Step-stress models under censoring
283(8)
9.3 Step stress models under hybrid censoring
291(6)
10 Applications in reliability
297(24)
10.1 Introduction
297(1)
10.2 Competing risks analysis
297(12)
10.3 Stress-strength models
309(1)
10.4 Optimal designs
310(4)
10.5 Reliability acceptance sampling plans
314(7)
11 Goodness-of-fit tests
321(10)
11.1 Introduction
321(1)
11.2 Progressive censoring
322(5)
11.3 Hybrid censoring
327(4)
12 Prediction methods
331(14)
12.1 Introduction
331(1)
12.2 Point prediction
331(11)
12.3 Interval prediction
342(3)
13 Adaptive progressive hybrid censoring
345(1)
13.1 Introduction
345(1)
132 Adaptive Type-II progressive hybrid censoring
346(7)
13.3 Inference for adaptive Type-II progressive hybrid censored data
349(2)
13.4 Adaptive Type-I progressive hybrid censoring
351(2)
Appendix
353(8)
A Geometrical objects
353(1)
B Distributions
354(3)
C B-splines and divided differences
357(4)
Bibliography 361(26)
Index 387
Narayanaswamy Balakrishnan is a distinguished university professor in the Department of Mathematics and Statistics at McMaster University Hamilton, Ontario, Canada. He is an internationally recognized expert on statistical distribution theory, and a book-powerhouse with over 24 authored books, four authored handbooks, and 30 edited books under his name. He is currently the Editor-in-Chief of Communications in Statistics published by Taylor & Francis. He was also the Editor-in-Chief for the revised version of Encyclopedia of Statistical Sciences published by John Wiley & Sons. He is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. In 2016, he was awarded an Honorary Doctorate from The National and Kapodistrian University of Athens, Athens, Greece. In 2021, he was elected as a Fellow of the Royal Society of Canada. Erhard Cramer is a Professor in the Institute for Statistics at RWTH Aachen University in Aachen, Germany. He has numerous publications to his credit and his research interests include order statistics, generalized order statistics, censoring methodology, B-spline theory, and statistical inference. He is a coauthor of the book The Art of Progressive Censoring: Applications to Reliability and Quality published by Birkhäuser, Boston, in 2014. Debasis Kundu is a Professor in the Department of Mathematics and Statistics at the Indian Institute of Technology Kanpur, India, which he joined in 1990. He had previously worked as Assistant Professor at the University of Texas at Dallas, USA, after completing his PhD in Statistics at Pennsylvania State University, USA. His research interests include statistical signal processing, nonlinear regression, distribution theory, statistical computing, and reliability and survival analysis.
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