Abstract

The joint censoring scheme is of great importance when the motive of study is to compare the relative merits of products in relation of their service times. In last few years, progressive censoring received considerable attention in order to save cost and time of the experiment. This paper deals with inferences for Lindley populations, when joint progressive type-II censoring scheme is applied on two samples in a joint manner. Here, the maximum likelihood estimators of parameters are derived along with their associated confidence intervals which are dependent on the Fisher’s information matrix. The boot-p and boot-t confidence intervals are also obtained. Bayes estimators of the unknown parameters assuming gamma priors are calculated. The concept of importance sampling technique and Gibbs sampling technique are used as the Bayes estimators cannot be calculated in closed form. HPD credible intervals are also constructed. A Monte Carlo simulation study is performed to measure the efficiency of the estimates. A real data set is given for illustrative purpose. Finally some criteria for an optimum censoring scheme are discussed.

摘要

当研究的动机是比较产品相对于其服务时间的相对优点时，联合审查方案非常重要。在过去的几年里，为了节省实验的成本和时间，渐进式审查受到了相当大的关注。当联合渐进 II 型审查方案以联合方式应用于两个样本时，本文处理对 Lindley 总体的推论。在这里，参数的最大似然估计量与它们相关的置信区间一起被推导出来，这些置信区间依赖于 Fisher 的信息矩阵。还获得了 boot-p 和 boot-t 置信区间。计算假设伽马先验的未知参数的贝叶斯估计量。由于贝叶斯估计量不能以封闭形式计算，因此使用重要性抽样技术和吉布斯抽样技术的概念。还构建了 HPD 可信区间。进行蒙特卡罗模拟研究以测量估计的效率。为了说明的目的，给出了一个真实的数据集。最后讨论了最佳审查方案的一些标准。