From Poisson Observations to Fitted Negative Binomial Distribution

Yingying Yang; Niloufar Dousti Mousavi; Zhou Yu; Jie Yang

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arXiv · 2404.07457

From Poisson Observations to Fitted Negative Binomial Distribution

Yingying Yang·Niloufar Dousti Mousavi·Zhou Yu·Jie Yang

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Abstract

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.

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Yingying Yang, Niloufar Dousti Mousavi, Zhou Yu, Jie Yang. 2024-04-11. From Poisson Observations to Fitted Negative Binomial Distribution. https://arxiv.org/abs/2404.07457

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