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Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data

机译：删失数据下威布尔分布的生存函数和失效率的贝叶斯分析

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摘要

The survival function of the Weibull distribution determines the probability that a unit or an individual will survive beyond a certain specified time while the failure rate is the rate at which a randomly selected individual known to be alive at time (t - 1) will die at time (t). The classical approach for estimating the survival function and the failure rate is the maximum likelihood method. In this study, we strive to determine the best method, by comparing the classical maximum likelihood against the Bayesian estimators using an informative prior and a proposed data-dependent prior known as generalised noninformative prior. The Bayesian estimation is considered under three loss functions. Due to the complexity in dealing with the integrals using the Bayesian estimator, Lindley's approximation procedure is employed to reduce the ratio of the integrals. For the purpose of comparison, the mean squared error (MSE) and the absolute bias are obtained. This study is conducted via simulation by utilising different sample sizes. We observed from the study that the generalised prior we assumed performed better than the others under linear exponential loss function with respect to MSE and under general entropy loss function with respect to absolute bias.
机译：Weibull分布的生存函数确定一个单元或个人将生存超过指定时间的概率，而故障率是在时间（t-1）处已知存活的随机选择的个体死亡的比率。时间（t）。估计生存函数和失败率的经典方法是最大似然法。在这项研究中，我们努力通过使用信息性先验和建议的数据相关先验（称为广义非信息先验）将经典最大似然与贝叶斯估计量进行比较，来确定最佳方法。在三个损失函数下考虑贝叶斯估计。由于使用贝叶斯估计器处理积分很复杂，因此采用Lindley逼近过程来减小积分的比率。为了比较，获得了均方误差（MSE）和绝对偏差。这项研究是通过利用不同的样本量进行模拟来进行的。从研究中我们观察到，假设的广义先验在相对于MSE的线性指数损失函数下和相对于绝对偏差的一般熵损失函数下均优于其他模型。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第10期|329489.1-329489.18|共18页
  • 作者

    Chris Bambey Guure; Noor Akma Ibrahim;

  • 作者单位

    Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia;

    Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia,Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia;

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