A Comparison of the Bayesian and Other Methods for Estimation of Reliability Function for Burr-XII Distribution
A Comparison of the Bayesian and Other Methods for Estimation of Reliability Function for Burr-XII Distribution
复制标题
贝叶斯法与其他 Burr-XII 分布可靠性函数估计方法的比较
DOI：
10.3844/jmssp.2012.42.48
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
N. Al
中科院分区：
文献类型：
--
作者：
Safaa Ali Nasir;N. Al
问题陈述：Burr-XII分布在生命周期事件数据的建模中得到了广泛的应用。它提供了一个在许多领域具有广泛应用的统计模型，其主要优点是能够在其他分布的生命时间事件背景下进行统计。传统的极大似然法是估计分布参数的常用方法。贝叶斯方法在与其他估计方法的竞争中受到了广泛的关注。在本研究中，我们探索并比较了两个参数Burr-XII分布的最大似然估计和中位数估计与可靠性函数的贝叶斯估计的性能。方法：提出了最大似然估计、中位数估计、利用杰弗里先验的贝叶斯估计、修正杰弗里先验和扩展杰弗里先验信息估计寿命时间Burr-XII分布的可靠性函数。我们用数值方法探讨了这些估计器在不同条件下的性能。通过仿真研究，比较了这些估计器在综合均方误差（IMSE）和综合平均绝对百分比误差（IMAPE）方面的性能。结果：对于所有不同的样本量，对于两个参数Burr-XII分布的移位参数的几个值以及对于Jeffery先验的扩展值，贝叶斯方法的估计量在大多数情况下比经典方法产生更小的IMSE，特别是在小尺寸的形状参数中。此外，在所有情况下，这两种方法的IMSE和IMAPE都随着样本量的增加而减小。结论：基于本仿真研究的结果，发现贝叶斯方法用于估计两参数Burr-XII分布的可靠度函数，相对于IMSE值，贝叶斯方法优于传统方法。
Problem statement: The Burr-XII distribution has been widely used especially in the modeling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood and median estimates with the Bayesian estimate of Reliability function for the two parameter Burr-XII distribution. Approach: The maximum likelihood estimation, median estimation, Bayesian using Jeffrey prior, modified Jeffery prior and extension of Jeffery prior information for estimation the Reliability function of Burr-XII distribution of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Integrated Mean Square Error (IMSE) and Integrated Mean Absolute Percentage Error (IMAPE). Results: For all the varying sample size, several values of the shifting parameter for the two parameter Burr-XII distribution and for the values for the extension of Jeffery prior, the estimator of Bayesian methods result in smaller IMSE compared to the classical methods in majority of the cases especially in small size of shape parameter. Also in all cases for both methods the IMSE and IMAPE decreases as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of reliability function for the two parameter Burr-XII distribution is found to be superior compared to the conventional methods with respect to IMSE values.