Abstract

A new distribution, the zero-inflated negative binomial-exponential (ZINB-E) distribution, is proposed. It is a mixture of a point mass at zero and a negative binomial-exponential (NB-E) distribution. The ZINB-E is an alternative distribution for count data with extra zeros and over-dispersion. We apply the method of maximum likelihood estimation for estimating parameters of the proposed distribution, and derive some of its mathematical properties. We also apply the proposed distribution to fit real data sets that have an excess of zero-count data. The result shows that the ZINB-E distribution is the best model for fitting data compared to the zero-inflated Poisson and zero-inflated negative binomial distributions.

中文翻译：

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零膨胀负二项式指数分布及其应用

摘要

提出了一种新的分布，即零膨胀负二项式指数（ZINB-E）分布。它是零质量点和负二项式指数（NB-E）分布的混合。ZINB-E是计数数据的替代分布，具有额外的零和过度分散。我们将最大似然估计方法用于估计提议分布的参数，并推导了其一些数学性质。我们还应用建议的分布来拟合具有零计数数据过多的真实数据集。结果表明，与零膨胀的Poisson分布和零膨胀的负二项式分布相比，ZINB-E分布是拟合数据的最佳模型。