多元零膨胀几何分布的参数估计
Parameter Estimation for the Multivariate Zero-Inflated Geometric Distribution
摘要: 本文探讨了多元计数数据中常见的零膨胀现象，并提出了一个针对多元零膨胀几何(ZIG)分布的理论与回归框架。该模型能够有效区分结构性零和额外零，适用于多元建模场景。文章系统推导了该分布的联合概率函数、累积分布函数、矩特征以及条件分布性质，基于期望最大化(EM)算法和Fisher评分算法建立了参数估计方法，并讨论了假设检验和置信区间构建问题。模拟研究表明，所提出的估计方法具有良好的有限样本性质。
Abstract: This paper addresses the common zero inflation phenomenon in multivariate count data and proposes a theoretical and regression framework for a multivariate zero-inflated geometric (ZIG) distribution. This model can effectively distinguish between structural zeros and extra zeros and is applicable to multivariate modeling scenarios. The article systematically derived the joint probability function, cumulative distribution function, moment characteristics, and conditional distribution properties of this distribution, established parameter estimation methods based on the EM algorithm and Fisher scoring algorithm, and discussed hypothesis testing and confidence interval construction issues. Simulation studies show that the proposed estimation method has good finite sample properties.
文章引用：连禹晴, 卢飞龙. 多元零膨胀几何分布的参数估计[J]. 应用数学进展, 2026, 15(5): 544-557. https://doi.org/10.12677/aam.2026.155250

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