Comparison of estimation methods for one-inflated positive Poisson distribution
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...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2021-01-01
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| Series: | Journal of Taibah University for Science |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/16583655.2021.2005910 |
| _version_ | 1818323611658747904 |
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| author | Razik Ridzuan Mohd Tajuddin Noriszura Ismail Kamarulzaman Ibrahim |
| author_facet | Razik Ridzuan Mohd Tajuddin Noriszura Ismail Kamarulzaman Ibrahim |
| author_sort | Razik Ridzuan Mohd Tajuddin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T11:15:27Z |
| format | Article |
| id | doaj.art-bd6b47651d8e4152b717e4d876bde073 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-12-13T11:15:27Z |
| publishDate | 2021-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-bd6b47651d8e4152b717e4d876bde0732022-12-21T23:48:37ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552021-01-0115186988110.1080/16583655.2021.20059102005910Comparison of estimation methods for one-inflated positive Poisson distributionRazik Ridzuan Mohd Tajuddin0Noriszura Ismail1Kamarulzaman Ibrahim2Department of Mathematical Sciences, Universiti Kebangsaan MalaysiaDepartment of Mathematical Sciences, Universiti Kebangsaan MalaysiaDepartment of Mathematical Sciences, Universiti Kebangsaan MalaysiaThis 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.http://dx.doi.org/10.1080/16583655.2021.2005910maximum likelihoodone-inflation indexordinary least squares methodratio of probabilityzero-truncated poisson |
| spellingShingle | Razik Ridzuan Mohd Tajuddin Noriszura Ismail Kamarulzaman Ibrahim Comparison of estimation methods for one-inflated positive Poisson distribution Journal of Taibah University for Science maximum likelihood one-inflation index ordinary least squares method ratio of probability zero-truncated poisson |
| title | Comparison of estimation methods for one-inflated positive Poisson distribution |
| title_full | Comparison of estimation methods for one-inflated positive Poisson distribution |
| title_fullStr | Comparison of estimation methods for one-inflated positive Poisson distribution |
| title_full_unstemmed | Comparison of estimation methods for one-inflated positive Poisson distribution |
| title_short | Comparison of estimation methods for one-inflated positive Poisson distribution |
| title_sort | comparison of estimation methods for one inflated positive poisson distribution |
| topic | maximum likelihood one-inflation index ordinary least squares method ratio of probability zero-truncated poisson |
| url | http://dx.doi.org/10.1080/16583655.2021.2005910 |
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