ABSTRACT

In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean time to failure, mean time between failure, availability and reliability function of consecutive linear and circular systems are studied. The hazard rate function can be increasing, decreasing, unimodal-bathtub, unimodal, bathtub, J and inverse J-shaped depending on its parameters values. After introducing the general class, two special models of the new family are discussed in detail. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. We also illustrate the importance of the new family by means of two distinctive real data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive and negative real data in many areas.

摘要

在本文中，提出了一种新的灵活的分布生成器。研究了它的一些基本性质，包括分位数、偏度、峰度、危险率函数、矩、平均偏差、平均故障时间、平均故障间隔时间、连续线性和循环系统的可用性和可靠性函数。危险率函数可以是递增、递减、单峰-浴缸、单峰、浴缸、J 和反 J 形，具体取决于其参数值。在介绍了通用类之后，详细讨论了新家族的两个特殊模型。最大似然和贝叶斯方法用于估计模型参数。进行了详细的模拟研究以检查最大似然和贝叶斯估计量的偏差和均方误差。我们还通过两个独特的真实数据集来说明新家庭的重要性。它可以作为现有统计文献中其他寿命分布的替代模型，用于对许多领域的正负真实数据进行建模。