Abstract

In this article, we consider the estimation problem of Unit Gompertz distribution with parameters α and β under the framework of dual generalized order statistics. This article is purely devoted to present the Bayesian view of estimation of Unit Gompertz distribution. For this purpose, we consider two widely popular approximation methods called Markov chain Monte Carlo and Lindley approximation methods. The results are derived under the symmetric (squared error) and asymmetric (Linear exponential and General entropy) loss functions. Since the order statistics and lower record values are the particular cases of the dual generalized order statistics, a simulation study is provided for order statistics and lower record values to observe the behavior of estimators. The average lengths of highest posterior density intervals of α, β, and R(t) are calculated for 95% confidence coefficient. Finally, real data applications are reported for lower record values and order statistics, separately, to show the practical aspects of the derived results.

摘要

在本文中，我们考虑参数为α和β的单位 Gompertz 分布的估计问题在对偶广义序统计的框架下。本文纯粹致力于介绍单位 Gompertz 分布估计的贝叶斯观点。为此，我们考虑两种广泛流行的近似方法，称为马尔可夫链蒙特卡罗和 Lindley 近似方法。结果是在对称（平方误差）和非对称（线性指数和广义熵）损失函数下得出的。由于阶次统计量和下记录值是对偶广义阶次统计量的特例，因此对阶次统计量和下记录值进行了模拟研究，以观察估计器的行为。α、β和R的最高后验密度区间的平均长度( t）是针对 95% 置信系数计算的。最后，分别报告较低记录值和订单统计的实际数据应用，以显示导出结果的实际方面。