El-Morshedy M, Eliwa M S, Nagy H
Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt.
J Appl Stat. 2019 Jul 8;47(2):354-375. doi: 10.1080/02664763.2019.1638893. eCollection 2020.
This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress-strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing-increasing-decreasing, increasing-decreasing-increasing, unimodal, bathtub, and -shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas.
本文介绍了一种新的双参数指数离散林德利分布。研究了其广泛的结构性质。这包括概率质量函数的形状、危险率函数、矩、偏度、峰度、应力-强度可靠性、平均剩余寿命、平均过去寿命、顺序统计量和L-矩统计量。危险率函数根据其参数值可以是递增、递减、先递减后递增再递减、先递增后递减再递增、单峰、浴盆形和反浴盆形。本文使用两种方法估计模型参数，即最大似然法和比例法。进行了详细的模拟研究，以检验最大似然估计和比例估计的偏差和均方误差。通过使用四个独特的数据集解释了所提出模型的灵活性。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实数据进行建模。
