ABSTRACT For and two independent random variables, upper values from the family of distributions with power hazard function are used to obtain the maximum likelihood and the Bayes estimators of . The Bayes estimator relies on the squared-error loss function given informative and non-informative prior distributions. It is obtained by either Lindley’s approximation, Tierney and Kadane’s method, or Monte Carlo simulation. The Monte Carlo simulation and Tierney and Kadane’s method have smaller mean squared errors than both Lindley’s approximation and the maximum likelihood estimator. The application for lung cancer data shows that the mortality risk by lung cancer is 40% lower for men than for women. The application for lifetimes of steels shows that steel specimen are 40% more likely to break up under 35.0 stress amplitude than under 35.5.

中文翻译：

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基于上记录值的具有幂风险函数的分布的可靠性 P(X > Y) 估计

摘要 对于 和 两个独立随机变量，使用具有幂风险函数的分布族的上限值来获得 的最大似然和贝叶斯估计量。贝叶斯估计器依赖于给定信息性和非信息性先验分布的平方误差损失函数。它是通过 Lindley 近似、Tierney 和 Kadane 方法或蒙特卡罗模拟获得的。Monte Carlo 模拟以及 Tierney 和 Kadane 的方法具有比 Lindley 近似和最大似然估计量更小的均方误差。肺癌数据的应用显示，男性因肺癌死亡的风险比女性低40%。钢寿命的应用表明，钢试样在 35.0 应力幅下比在 35.5 下断裂的可能性高 40%。