In this article, we proposed an inverse Lindley distribution and studied itsfundamental properties such as quantiles, mode, stochastic ordering and entropymeasure. The proposed distribution is observed to be a heavy-taileddistribution and has a upside-down bathtub shape for its failure rate. Further,we proposed its applicability as a stress-strength reliability model forsurvival data analysis. The estimation of stress-strength parameters and$R=P[X>Y]$, the stress-strength reliability has been approached by bothclassical and Bayesian paradigms. Under Bayesian set-up, non-informative(Jeffrey) and informative (gamma) priors are considered under a symmetric(squared error) and a asymmetric (entropy) loss functions, and aLindley-approximation technique is used for Bayesian computation. The proposedestimators are compared in terms of their mean squared errors through asimulation study. Two real data sets representing survival of Head and Neckcancer patients are fitted using the inverse Lindley distribution and used toestimate the stress-strength parameters and reliability.
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机译:在本文中,我们提出了逆Lindley分布,并研究了其基本性质,例如分位数,模式,随机有序性和熵测度。观察到建议的分布是一个重尾分布,其故障率具有倒置的浴缸形状。此外,我们提出了其作为生存数据分析的应力强度可靠性模型的适用性。应力强度参数和$ R = P [X> Y] $的估计,应力强度可靠性已通过经典和贝叶斯范式进行了研究。在贝叶斯设置下,考虑非对称(平方误差)和非对称(熵)损失函数下的非信息先验(Jeffrey)和信息先验(γ),并且贝叶斯计算采用林德利逼近技术。通过模拟研究,对建议的估计器进行均方误差比较。使用逆Lindley分布拟合了代表Head和Neckcancer患者生存的两个真实数据集,并用于估计压力强度参数和可靠性。
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