Screen LibraryThe stress-strength model and its generalizations : theory and applications /
This important book presents developments in a remarkable field of inquiry in statistical/probability theory - the stress-strength model. Many papers in the field include the enigmatic "words" P(X<Y) - or something similar - in the title. This reflects the long-established concept of or...
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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | ; |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore ; River Edge, N.J. : |
| Publication Dates: | 2003. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/5015#t=toc |
| Summary: |
This important book presents developments in a remarkable field of inquiry in statistical/probability theory - the stress-strength model. Many papers in the field include the enigmatic "words" P(X<Y) - or something similar - in the title. This reflects the long-established concept of ordering of distributions. The basic impetus for the study carried out by the authors of this book is the general concept of stress-strength as an interpretation of the P(X<Y) relationships, which leads to applications in reliability engineering, economics and modern medicine. The Stress-Strength Model and Its Generalizations collects and digests theoretical and practical results on the theory and applications of the stress-strength relationships in industrial and economic systems - results that have been scattered in the literature during the last 40-odd years - and augments and presents them for the first time in a unified manner suitable for practitioners as well as probabilists and theoretical and applied statisticians. |
| Carrier Form: | 1 online resource (xvii,253pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 233-249) and index. |
| ISBN: | 9789812564511 (electronic bk.) |
| CLC: | O346.2 |
| Contents: | ch. 1. The stress-strength models. Mathematics, history, and applications. 1.1. What are the stress-strength models? 1.2. Motivation and mathematical formulations. 1.3. Stress-strength models: history and geography. 1.4. Applications -- ch. 2. The theory and some useful approaches. 2.1. The maximum likelihood estimators. 2.2. Unbiased estimation. 2.3. Bayes and empirical Bayes estimation of R. 2.4. Interval estimation. 2.5. Transformation methods. 2.6. Exercises -- ch. 3. Parametric point estimation. 3.1. The maximum likelihood estimation (univariate case). 3.2. Unbiased estimation (univariate case). 3.3. Bayes and empirical Bayes estimation (univariate case). 3.4. Elliptical distributions. 3.5. The multivariate normal distribution. 3.6 Bivariate exponential distributions (BVED). 3.7 Discrete distributions. 3.8. Exercises -- ch. 4. Parametric statistical inference. 4.1. Confidence intervals based on exact distributions. 4.2. Asymptotic confidence intervals. 4.3. Bayesian credible sets. 4.4. Hypothesis testing. 4.5. Bootstrap. 4.6. Exercises -- ch. 5. Nonparametric models. 5.1. Point estimation of R = P(X<Y). 5.2. Estimation of the variance of . 5.3. Interval estimation of R. 5.4. Nonparametric Bayes and empirical Bayes estimation. 5.5. Probability design approach to estimation of R. 5.6. Exercises -- ch. 6. Some selected special cases. 6.1. Stress-strength models for system reliability. 6.2. Estimation of P[symbol]. 6.3. Linear models formulations for stress-strength systems. 6.4. Stress-strength models with grouped and categorical data. 6.5. Stochastic processes formulations of stress-strength systems. 6.6. Exercises -- ch. 7. Applications and examples. 7.1. Applicability of the stress-strength model. 7.2. Engineering and military applications of the stress-strength model. 7.3. Applications in medicine and psychology. 7.4. ROC curves analysis. 7.5. Some other applications. |