Connections of the Poisson weight function to overdispersion and underdispersion

详细信息    查看全文

• 作者：Cé ; lestin C. Kokonendji ; Dominique Mizè ; re ; N. Balakrishnan
• 关键词：Poisson distribution ; Weighted Poisson distribution ; Size-biased Poisson distribution ; COM-Poisson distribution ; Dual distribution ; Logconcavity ; Logconvexity ; Overdispersion ; Underdispersion ; Natural exponential family
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2008
• 出版时间：1 May 2008
• 年：2008
• 卷：138
• 期：5
• 页码：1287-1296
• 全文大小：173 K

文摘

In this paper, we establish several connections of the Poisson weight function to overdispersion and underdispersion. Specifically, we establish that the logconvexity (logconcavity) of the mean weight function is a necessary and sufficient condition for overdispersion (underdispersion) when the Poisson weight function does not depend on the original Poisson parameter. We also discuss some properties of the weighted Poisson distributions (WPD). We then introduce a notion of pointwise duality between two WPDs and discuss some associated properties. Next, we present some illustrative examples and provide a discussion on various Poisson weight functions used in practice. Finally, some concluding remarks are made.