The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference.
The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc.
| Preface |
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iii | |
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1 | (39) |
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1.1 Reliability analysis and information theory |
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1 | (2) |
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1.2 Basic reliability functions |
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3 | (7) |
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1.3 Quantile-based reliability functions |
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10 | (4) |
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1.4 Quantile function models |
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14 | (3) |
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1.5 Ageing and associated criteria |
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17 | (1) |
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1.6 Concepts based on hazard rate |
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18 | (3) |
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1.7 Concepts based on residual life |
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21 | (2) |
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1.8 Classes based on survival function |
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23 | (2) |
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1.9 Concepts in reversed time |
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25 | (1) |
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26 | (2) |
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1.11 Log concave and convex distributions |
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28 | (2) |
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1.12 Weighted distributions |
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30 | (4) |
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34 | (6) |
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40 | (62) |
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40 | (1) |
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2.2 Definition and properties of entropy |
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41 | (3) |
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44 | (3) |
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47 | (11) |
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58 | (4) |
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2.6 Quantile-based residual entropy |
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62 | (16) |
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2.7 Weighted residual entropy |
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78 | (3) |
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81 | (5) |
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2.9 Estimation and testing |
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86 | (5) |
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91 | (11) |
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102 | (41) |
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102 | (2) |
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3.2 Properties of past entropy |
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104 | (16) |
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3.3 Past quantile entropy |
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120 | (6) |
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126 | (4) |
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3.5 Weighted past entropy |
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130 | (3) |
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133 | (2) |
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135 | (8) |
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143 | (38) |
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143 | (1) |
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144 | (25) |
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169 | (7) |
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176 | (3) |
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179 | (2) |
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181 | (31) |
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181 | (1) |
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5.2 Kullback-Leibler divergence |
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182 | (16) |
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198 | (7) |
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205 | (1) |
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206 | (3) |
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209 | (1) |
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210 | (2) |
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212 | (27) |
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212 | (1) |
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6.2 Inaccuracy of residual lives |
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213 | (14) |
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6.3 Quantile-based inaccuracy |
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227 | (7) |
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6.4 Past inaccuracy measure |
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234 | (2) |
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236 | (3) |
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239 | (41) |
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239 | (3) |
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7.2 Cumulative entropy of residual life |
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242 | (7) |
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7.3 Cumulative residual entropy of order n |
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249 | (4) |
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7.4 Dynamic version of Cn |
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253 | (7) |
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7.5 Weighted cumulative residual entropy |
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260 | (5) |
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265 | (3) |
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7.7 Quantile-based cumulative entropy |
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268 | (8) |
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276 | (4) |
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8 Generalized Cumulative Entropy and Divergence |
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280 | (39) |
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280 | (1) |
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8.2 Survival and failure entropies |
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280 | (7) |
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8.3 Cumulative divergence |
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287 | (5) |
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8.4 Cumulative Tsallis entropy |
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292 | (8) |
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8.5 Cumulative Varma's entropy |
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300 | (2) |
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8.6 Cumulative residual inaccuracy |
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302 | (5) |
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8.7 Generalized cumulative residual entropy |
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307 | (12) |
| References |
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319 | (24) |
| Index |
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343 | |
N. Unnikrishnan Nair gained his Ph.D from the University of Kerala, India and was conferred the degree of Doctor of Humane Letters by Juniata College, USA. He is a Fellow of the Indian Society for Probability and Statistics and its past President. He was also a member of the International Statistical Institute. Nair was the Professor and Chair of the Department of Statistics of the Cochin University of Science and Technology, India, and Dean, Faculty of Science. He also served the University as its Vice Chancellor. He has published six books of which he is the leading author of two recent titles, Quantile-based Reliability Analysis by Birkhauser and Reliability Modeling and Analysis in Discrete Time by Academic Press. He has published over 170 papers in refereed international journals.
S.M. Sunoj gained his Ph.D from the Cochin University of Science and Technology, India. He is the Professor of Department of Statistics, Cochin University of Science and Technology. He has published over 65 papers in refereed international journals. He is an elected member of the International Statistical Institute. He is currently the Associate Editor of the Journal of the Indian Society for Probability and Statistics, India. His areas of research include distribution theory, reliability theory and information measures.
G. Rajesh is the Professor of the Department of Statistics, Cochin University of Science and Technology, India. He received his Ph.D from the Department of Statistics, Cochin University of Science and Technology, India. His main areas of research include distribution theory, information measures and non-parametric inferences. He has published more than 50 research papers in refereed international journals.
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