基于上记录范围的指数分布的贝叶斯推断
Bayesian Inference For Exponential Distribution Based On Upper Record Range
AI总结：
本文研究了基于上记录范围的指数分布尺度参数的贝叶斯估计，采用点估计和区间估计方法，利用不同损失函数获得点估计，并通过同调摄动法求得最短贝叶斯区间，同时满足线性估计的可接受性条件。
摘要：
本文研究了基于上记录范围的指数分布尺度参数的贝叶斯估计，分为两个步骤：点估计和区间估计。首先考虑二次损失、平方误差和绝对误差损失函数，获得贝叶斯点估计。接着利用同调摄动法求得最短贝叶斯区间（高后验密度区间）和等尾贝叶斯区间。此外，努力满足基于上记录范围统计量的线性估计的可接受性条件。最后，通过数值示例和模拟进行了展示。
英文摘要：
This paper deals with Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). This has been done in two steps; point and interval. In the first step the quadratic, squared error and absolute error, loss functions have been considered to obtain Bayesian-point estimations. Also in the next step the shortest Bayes interval (Hight Posterior Density interval) and Bayes interval with equal tails based on upper record range have been found. Therefore, the Homotopy Perturbation Method(HPM) has been applied to obtain the limits of Hight Posterior Density intervals. Moreover, efforts have been made to meet the admissibility conditions for linear estimators based on upper record range of the form mRn+d by obtained Bayesian point estimations. So regarding the consideration of loss functions, the prior distribution between the conjunction family has been chosen to be able to produce the linear estimations from upper record range statistics. Finally, some numerical examples and simulations have been presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
