Abstract

The characteristic of count data that have a high frequency of zeros and ones can be considered under a zero-one inflated distribution. In this article, we present a zero-one inflated negative binomial - beta exponential distribution to analyze for such data. This distribution shows that it is extended the mixture negative binomial with beta exponential distributions, was proposed by Pudprommarat, Bodhisuwan, and Zeephongsekul (2012). Some important properties of this distribution are discussed, which include probability mass function, moment generating function, moment about the origin, mean and variance. Additionally, some sub-models are presented. Its parameters are also derived based on the maximum likelihood estimation procedure. The applicability of the proposed distribution is demonstrated for fitting to three real data sets. We also evaluate the abilities of model selection relying on the negative log-likelihood, Akaike information criterion, mean absolute error, root mean squared error, discrete Kolmogorov–Smirnov test and Anderson-Darling tests. Results from this study indicate the zero-one inflated negative binomial - beta exponential distribution has shown the best fit for these data sets when it is compared with some sub-models and the zero-one inflated of traditional distributions.

摘要

计数数据具有高频率的零和一的特征可以考虑在零一膨胀分布下。在本文中，我们提出了一个零一膨胀负二项式 - 贝塔指数分布来分析此类数据。该分布表明它扩展了具有 beta 指数分布的混合负二项式，由 Pudprommarat、Bodhisuwan 和 Zeephongsekul (2012) 提出。讨论了该分布的一些重要性质，包括概率质量函数、矩生成函数、关于原点的矩、均值和方差。此外，还介绍了一些子模型。它的参数也是基于最大似然估计程序得出的。所提出的分布的适用性被证明可用于拟合三个真实数据集。我们还根据负对数似然、Akaike 信息准则、平均绝对误差、均方根误差、离散 Kolmogorov-Smirnov 检验和 Anderson-Darling 检验来评估模型选择的能力。这项研究的结果表明，当与一些子模型和零一膨胀的传统分布进行比较时，零一膨胀负二项式 - β 指数分布已显示出最适合这些数据集。