The Exponentiated Power Generalized Weibull: Properties and Applications

Abstract We propose a new lifetime model called the exponentiated power generalized Weibull (EPGW) distribution, which is obtained from the exponentiated family applied to the power generalized Weibull (PGW) distribution. It can also be derived from a power transform on an exponentiated Nadarajah-Haghighi random variable. Since several structural properties of the PGW distribution have not been studied, they can be obtained from those of the EPGW distribution. The model is very flexible for modeling all common types of hazard rate functions. It is a very competitive model to the well-known Weibull, exponentiated exponential and exponentiated Weibull distributions, among others. We also give a physical motivation for the new distribution if the power parameter is an integer. Some of its mathematical properties are investigated. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters.

摘要 我们提出了一种名为指数化幂广义威布尔（exponentiated power generalized Weibull, EPGW）分布的全新寿命模型。该分布可通过作用于幂广义威布尔（power generalized Weibull, PGW）分布的指数化族构造得到，也可通过对指数化纳达拉杰-哈格希（exponentiated Nadarajah-Haghighi）随机变量实施幂变换推导得出。鉴于目前尚未对PGW分布的多项结构性质展开研究，相关性质可通过EPGW分布的对应性质推导获得。该模型在拟合各类常见风险率函数方面具备极强灵活性，相较于经典的威布尔分布、指数化指数分布以及指数化威布尔分布等模型，展现出显著的竞争力。当幂参数为整数时，我们还为该新分布给出了物理解释。本文对该模型的部分数学性质展开了研究，讨论了基于极大似然法的模型参数估计方案，并提供了两组真实数据集应用实例。此外，我们开展了模拟研究以验证模型参数极大似然估计量的准确性。