ABSTRACT

In the current paper, the maximum likelihood and Bayes estimators for the two shape parameters of the Burr Type III distribution are investigated based on adaptive Type II progressive hybrid censored data. The maximum likelihood estimators are provided for estimating the unknown parameters. The existence and uniqueness of the maximum likelihood estimation are shown using the graphical method. The Bayes estimates are obtained under two loss functions using the Lindley’s method and Metropolis-Hastings sampling procedure. Further, approximate and Bayesian intervals are constructed. Monte Carlo simulation study is performed to check the accuracy of the estimates and compare the performance of the proposed confidence intervals. Also, the nano droplet data is analyzed to illustrate the application and development of the inference methods.

摘要

在当前论文中，基于自适应II型渐进混合检查数据，研究了Burr III型分布的两个形状参数的最大似然和贝叶斯估计。提供最大似然估计器用于估计未知参数。使用图形方法显示了最大似然估计的存在和唯一性。使用Lindley方法和Metropolis-Hastings抽样程序在两个损失函数下获得贝叶斯估计。此外，构造近似间隔和贝叶斯间隔。进行了蒙特卡洛模拟研究，以检查估计的准确性并比较建议置信区间的性能。此外，分析了纳米液滴数据以说明推理方法的应用和发展。