A new lifetime distribution, called exponential doubly Poisson distribution, is proposed with decreasing, increasing, and upside-down bathtub-shaped hazard rates. One of the reasons for introducing the new distribution is that it can describe the failure time of a system connected in the form of a parallel-series structure. Some properties of the proposed distribution are addressed. Four methods of estimation for the involved parameters are considered based on progressively type II censored data. These methods are maximum likelihood, moments, least squares, and weighted least squares estimations. Through an extensive numerical simulation, the performance of the estimation methods is compared based on the average of mean squared errors and the average of absolute relative biases of the estimates. Two real datasets are used to compare the proposed distribution with some other well-known distributions. The comparison indicates that the proposed distribution is better than the other distributions to match the data provided.

中文翻译：

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渐进式II删失下平行系列结构的新寿命分布推断

提出了一种新的寿命分布，称为指数双倍Poisson分布，具有降低，增加和倒置的浴缸状危险率。引入新分布的原因之一是它可以描述以并行串联结构形式连接的系统的故障时间。解决了建议的分布的某些属性。基于渐进式II型审查数据，考虑了四种估计所涉及参数的方法。这些方法是最大似然，矩，最小二乘和加权最小二乘估计。通过广泛的数值模拟，根据均方误差的平均值和估算值的绝对相对偏差的平均值来比较估算方法的性能。使用两个真实的数据集将建议的分布与其他一些知名的分布进行比较。比较表明，建议的分布要比其他分布更好以匹配提供的数据。