Chesneau Christophe, Bakouch Hassan S, Hussain Tassaddaq, Para Bilal A
LMNO, University of Caen-Normandie, Caen, France.
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.
J Appl Stat. 2020 Jan 9;48(1):124-137. doi: 10.1080/02664763.2019.1711364. eCollection 2021.
In this paper, a new two-parameter discrete distribution is introduced. It belongs to the family of the weighted geometric distribution (GD), with the feature of using a particular trigonometric weight. This configuration adds an oscillating property to the former GD which can be helpful in analyzing the data with over-dispersion, as developed in this study. First, we present the basic statistical properties of the new distribution, including the cumulative distribution function, hazard rate function and moment generating function. Estimation of the related model parameters is investigated using the maximum likelihood method. A simulation study is performed to illustrate the convergence of the estimators. Applications to two practical datasets are given to show that the new model performs at least as well as some competitors.
本文介绍了一种新的双参数离散分布。它属于加权几何分布（GD）族，其特点是使用特定的三角权重。这种配置为原有的GD增添了一种振荡特性，这有助于在本研究中对具有过度离散的数据进行分析。首先，我们给出了新分布的基本统计性质，包括累积分布函数、风险率函数和矩生成函数。使用最大似然法研究了相关模型参数的估计。进行了一项模拟研究以说明估计量的收敛性。给出了两个实际数据集的应用，以表明新模型的表现至少与一些竞争模型一样好。
