In this paper, we introduce a new flexible distribution called the Weibull Marshall-Olkin power-Lindley (WMOPL) distribution to extend and increase the flexibility of the power-Lindley distribution to model engineering related data. The WMOPL has the ability to model lifetime data with decreasing, increasing, J-shaped, reversed-J shaped, unimodal, bathtub, and modified bathtub shaped hazard rates. Various properties of the WMOPL distribution are derived. Seven frequentist estimation methods are considered to estimate the WMOPL parameters. To evaluate the performance of the proposed methods and provide a guideline for engineers and practitioners to choose the best estimation method, a detailed simulation study is carried out. The performance of the estimators have been ranked based on partial and overall ranks. The performance and flexibility of the introduced distribution are studied using one real data set from the field of engineering. The data show that the WMOPL model performs better than some well-known extensions of the power-Lindley and Lindley distributions.

在本文中，我们引入了一种新的灵活分布，称为 Weibull Marshall-Olkin power-Lindley (WMOPL) 分布，以扩展和增加 power-Lindley 分布对工程相关数据建模的灵活性。WMOPL 能够对具有递减、递增、J 形、倒 J 形、单峰、浴盆和修正浴盆形危险率的寿命数据进行建模。导出了 WMOPL 分布的各种属性。考虑了七种频率论估计方法来估计 WMOPL 参数。为了评估所提出方法的性能并为工程师和从业人员选择最佳估计方法提供指导，进行了详细的模拟研究。估计器的性能已根据部分和整体排名进行排名。使用来自工程领域的一组真实数据来研究引入的分布的性能和灵活性。数据表明，WMOPL 模型的性能优于一些众所周知的幂-林德利分布和林德利分布的扩展。