Abstract

In this paper, the positive negative binomial-Lindley distribution is used to model count data for which the value zero cannot occur, which means that the NB-L distribution has to be adjusted for the missing zeros. We introduce and investigate some characteristics of the proposed distributions, such as the mean and variance. For the simulation, the parameters of the proposed distributions are estimated based on the maximum likelihood estimation method. We consider the efficiency of this parameter estimation method based on the mean squared error. It is applied in two applications; the positive NB-L distribution provides a better fit than the zero-truncated Poisson and the zero-truncated Poisson–Lindley distributions.

中文翻译：

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正负二项式-Lindley分布及其应用

摘要

在本文中，正负二项式-Lindley分布用于对不能出现零值的计数数据进行建模，这意味着必须针对缺失的零调整NB-L分布。我们介绍并研究了建议分布的一些特征，例如均值和方差。为了进行仿真，基于最大似然估计方法估计了建议分布的参数。我们考虑基于均方误差的参数估计方法的效率。它被应用在两个应用程序中。正NB-L分布比零截断的Poisson分布和零截断的Poisson-Lindley分布具有更好的拟合度。