An Exceptional Generalization of the Poisson Distribution

• 作者: Per-Erik Hagmark
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: COUNT Data Gamma Function POISSON GENERALIZATION DISCRETIZATION Modeling Over/Under-Dispersion Zero-Inflation/Deflation
• 年，卷（期）: tjxqkyw_2012,（3）
• 页码范围: 313-318
• 页数: 6页
• 分类号: O1

摘要

A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortment of qualities. For example, the mean is the main model parameter;any possible non-trivial variance or zero probability can be attained by changing the other model parameter;and all distributions are visually natural-shaped. Thus, exact modeling to any degree of over/under-dispersion or zero-inflation/deflation is possible.