Comparison of estimation methods for one-inflated positive Poisson distribution

Journal of Taibah University for Science

Noriszura Ismail¹  Razik Ridzuan Mohd Tajuddin¹  Kamarulzaman Ibrahim¹ 

[1] Department of Mathematical Sciences, Universiti Kebangsaan Malaysia;

关键词: maximum likelihood;    one-inflation index;    ordinary least squares method;    ratio of probability;    zero-truncated poisson;   

DOI  :  10.1080/16583655.2021.2005910

来源: DOAJ

【 摘 要 】

This paper aims to propose estimation methods for one-inflated positive Poisson (OIPP) distribution and compare their properties in terms of unbiasedness, consistency, efficiency and deficiency. All estimators considered in the study are asymptotically unbiased and consistent. The maximum likelihood estimator (MLE) for the OIPP distribution is asymptotically normal. When compared to the MLE, the ordinary least square estimator (OLSE) is the most efficient, followed by the method of moments estimator (MME) and the ratio of probability estimator (RPE). A novel one-inflation index was also proposed to assess the presence of excess ones in the dataset for the positive Poisson distribution to determine whether a one-inflated distribution is required for model fitting. A real dataset with a large number of ones, as identified by the proposed one-inflation index, was used for model fitting. It is found that the OLSE and MLE are the best estimators for an OIPP distribution.

【 授权许可】

Unknown