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On progressively censored generalized inverted exponential distribution

机译：关于渐进删失广义逆指数分布

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摘要

A generalized version of inverted exponential distribution (IED) is considered in this paper. This lifetime distribution is capable of modeling various shapes of failure rates, and hence various shapes of aging criteria. The model can be considered as another useful two-parameter generalization of the IED. Maximum likelihood and Bayes estimates for two parameters of the generalized inverted exponential distribution (GIED) are obtained on the basis of a progressively type-Ⅱ censored sample. We also showed the existence, uniqueness and finiteness of the maximum likelihood estimates of the parameters of GIED based on progressively type-Ⅱ censored data. Bayesian estimates are obtained using squared error loss function. These Bayesian estimates are evaluated by applying the Lindley's approximation method and via importance sampling technique. The importance sampling technique is used to compute the Bayes estimates and the associated credible intervals. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. Monte Carlo simulations are performed to compare the performances of the proposed methods and a data set has been analyzed for illustrative purposes.
机译：本文考虑了广义的倒指数分布（IED）。此寿命分布能够对各种形状的故障率进行建模，从而对各种形式的老化标准进行建模。该模型可以看作是IED的另一个有用的两参数概括。在渐进Ⅱ型删失样本的基础上，获得了广义倒指数分布（GIED）两个参数的最大似然和贝叶斯估计。我们还基于渐进式Ⅱ类删失数据显示了GIED参数最大似然估计的存在性，唯一性和有限性。使用平方误差损失函数获得贝叶斯估计。这些贝叶斯估计值是通过使用Lindley近似方法并通过重要性抽样技术来评估的。重要度采样技术用于计算贝叶斯估计和相关的可信区间。我们根据观察到的样本进一步考虑贝叶斯预测问题，并提供适当的预测间隔。进行蒙特卡洛模拟以比较所提出方法的性能，并且出于说明目的对数据集进行了分析。

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