The log-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta distribution. This distribution has a simple structure and possesses useful theoretical properties relevant in insurance. Classical estimation methods have been well studied. We introduce estimation of parameters from Bayesian point of view for this distribution. Explicit structure of stress–strength reliability and its inference under both classical and Bayesian set-ups is addressed. Extensive simulation studies show marked improvement with Bayesian approach over classical given reasonable prior information. An application of a useful metric of discrepancy derived from stress–strength reliability is considered and computed for two categories of firm with respect to a certain financial indicator.

中文翻译：

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用log-Lindley分布估计应力-强度可靠性

最近在文献中引入了 log-Lindley 分布，作为 Beta 分布的可行替代方案。这种分布具有简单的结构，并具有与保险相关的有用理论特性。经典的估计方法已经得到很好的研究。我们从贝叶斯的角度介绍了这个分布的参数估计。应力强度可靠性的显式结构及其在经典和贝叶斯设置下的推断得到了解决。广泛的模拟研究表明，贝叶斯方法比给定合理先验信息的经典方法有显着改进。考虑并计算两类公司关于某个财务指标的有用差异度量的应用，该度量源自压力-强度可靠性。