A Bayes interval estimation for an exponential parameter Theta in a model of random censoring with incomplete information is investigated. The instant of item failure is observed if it occurs before a randomly chosen inspection time and the failure was signaled; otherwise, the experiment is terminated at the instant of inspection. An explicit expression for the posterior PDF (probability distribution function) of the parameter is derived, and a normal approximation to it based on Taylor expansion near the maximum likelihood estimate is suggested. The results of an extension simulation showed that the reparametrization Theta /sub 1/=log Theta appreciably increases the accuracy of the normal approximation. Highly accurate highest posterior density intervals for Theta /sub 1/ are derived in a closed form for a normal prior for Theta /sub 1/ or, equivalently, for the lognormal prior on Theta .
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机译:研究了信息不完整的随机删失模型中指数参数Theta的贝叶斯区间估计。如果项目故障发生在随机选择的检查时间之前并发出故障信号,则将对其进行观察。否则,实验将在检查时终止。推导了该参数的后部PDF(概率分布函数)的明确表达式,并提出了基于最大似然估计附近的泰勒展开的正态近似。扩展仿真的结果表明,重新参数化Theta / sub 1 / = log Theta明显提高了法线逼近的准确性。对于Theta / sub 1 /的法线先验,或等效地,对于Theta的对数法线的先验,以封闭的形式导出Theta / sub 1 /的高精度最高后验密度区间。
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