Statistical Inference for the Zero Modification Parameter in Zero-Modified Poisson Models

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  • Daidoji Kasumi
    Safety Management Department, Corporate Medical Affairs Headquarters,Eisai Co., Ltd.
  • Iwasaki Manabu
    Department of Computer and Information Science, Seikei University
  • Yamashita Haruka
    Graduate School of Science and Technology, Seikei University

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  • ゼロ修正されたポアソン分布におけるゼロ修正パラメータの統計的推測
  • ゼロ シュウセイ サレタ ポアソン ブンプ ニ オケル ゼロ シュウセイ パラメータ ノ トウケイテキ スイソク

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Abstract

For count data of rare events, a Poisson distribution is most frequently used to model the phenomenon under consideration. However, it is sometimes observed in various applications that the zero count is too many or too few than the count expected under the usual Poisson model. In such cases so-called zero-modified Poisson (ZMP) distributions would be fitted to the observed data. This paper discusses the performance of estimation procedures of the parameter involved in the ZMP distribution. First we attempt to clarify the meaning of the zero-modification parameter in the zero-deflated Poisson (ZDP) distribution in comparison to the zero-inflated Poisson (ZIP) distribution. After reviewing the maximum likelihood estimation procedures for the parameters of ZMP models, a simulation study is conducted to assess the performance of confidence intervals of the zero-modification parameter from the viewpoint of coverage probability. It is found that when sample size is small and the Poisson parameter is small, the performance of interval estimation is not so well. However, for the case of moderate and large sample sizes the coverage probabilities of the confidence intervals are almost equal to the nominal confidence coefficient.

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