## The Stress-strength Model and Its Generalizations: Theory and ApplicationsThis important book presents developments in a remarkable field ofinquiry in statistical/probability theory the stressOCostrengthmodel.Many papers in the field include the enigmatic words"P"("X"Y") or something similar in thetitle." |

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### Contents

1 | |

11 | |

Parametric Point Estimation | 47 |

Parametric Statistical 1nference | 109 |

Nonparametric Models | 139 |

Some Selected Special Cases | 169 |

Applications and Examples | 201 |

233 | |

251 | |

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### Common terms and phrases

applications approximate assume assumption asymptotic confidence interval asymptotically normal Bayes estimator Bayesian beta distribution binomial bivariate bootstrap Burr type BVED calculations Casella Chapter components confidence interval confidence intervals based defined Denote density Derive the MLE Dirichlet process Distribution Let Enis and Geisser equation estimation of P(X exact confidence intervals example exponential distribution expression follows formula function Fx(x gamma distribution given Guttman Halperin Hence hypergeometric series independent normal variables independent random variables inequality integration interval estimation Ivshin and Lumelskii Jeffreys's prior known lower confidence bound Lumelskii 1995 matching prior matrix method multivariate nonparametric Note observations obtain p-value Pareto distribution pivotal quantity posterior pdf probability problem random vector Reiser respectively ROC curve Section strength stress stress-strength models sufficient statistic system reliability T-distribution technique Theorem tion transformation two-parameter exponential UMVUE unbiased estimator unknown values Var(fi variance Weibull Weibull Distribution

### Popular passages

Page v - century a special meaning to a modern person. We all are continuously under stress, and, alas, not always have the “strength” to overcome it. The stress-strength relationship is nowadays studied in many branches of science such as psychology, medicine, pedagogy, etc. and the pharmaceutical industry accumulates

Page v - alleviate psychological stresses. Broadly speaking, the term stress is used nowadays in two different meanings: 1) structural, mechanical (or engineering) stress studied in the engineering discipline called “strength of materials”, and more

Page v - of gunshot - which the brain interprets as dangerous”. Another way of describing this concept is “a demand, threat or other event that requires an individual to

Page 2 - strength” of the component available to overcome the stress. According to this simplified scenario if the stress exceeds the strength

Page 2 - appears in the title of Church and Harris (1970) . This is the earliest date in our bibliography though earlier

Page 3 - tail of the strength distribution can make the failure probability far higher than may be desirable, particularly,