From Poisson Observations to Fitted Negative Binomial Distribution
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910103587782656 |
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| author | Yang, Yingying Mousavi, Niloufar Dousti Yu, Zhou Yang, Jie |
| author_facet | Yang, Yingying Mousavi, Niloufar Dousti Yu, Zhou Yang, Jie |
| contents | The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a negative binomial distribution with extreme parameter values, and existing maximum likelihood estimation procedures for the negative binomial distribution may fail or produce unstable estimates. To address this issue, we develop a new algorithm for computing the maximum likelihood estimate of negative binomial parameters, which is more efficient and more accurate than existing methods. We further extend negative binomial distributions with a new parameterization to cover Poisson distributions as a special class. We provide theoretical justifications showing that, when applied to a Poisson data, the estimated parameters of the extended negative binomial distribution can consistently recover the true Poisson distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Poisson Observations to Fitted Negative Binomial Distribution Yang, Yingying Mousavi, Niloufar Dousti Yu, Zhou Yang, Jie Statistics Theory Computation The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a negative binomial distribution with extreme parameter values, and existing maximum likelihood estimation procedures for the negative binomial distribution may fail or produce unstable estimates. To address this issue, we develop a new algorithm for computing the maximum likelihood estimate of negative binomial parameters, which is more efficient and more accurate than existing methods. We further extend negative binomial distributions with a new parameterization to cover Poisson distributions as a special class. We provide theoretical justifications showing that, when applied to a Poisson data, the estimated parameters of the extended negative binomial distribution can consistently recover the true Poisson distribution. |
| title | From Poisson Observations to Fitted Negative Binomial Distribution |
| topic | Statistics Theory Computation |
| url | https://arxiv.org/abs/2404.07457 |