Overdispersed Count Data Using Negative Binomial-Quasi XGamma Distribution

Siriporn Samutwachirawong

Authors

Siriporn Samutwachirawong Program in Statistics and Information Management, Faculty of Science, Maejo University.

Keywords:

negative binomial distribution, quasi-xgamma distribution, mixed distribution, count data, overdispersion

Abstract

This paper introduces the negative binomial-quasi xgamma (NB-QX) distribution, a three-parameter model derived by mixing the negative binomial and quasi xgamma distributions. The NB-QX distribution offers significant flexibility in analyzing overdispersed count data and subsumes the negative binomial-gamma distribution as a special case. We derive its fundamental properties, including the probability mass function, factorial moments, mean, and variance. Parameter estimation is conducted via the maximum likelihood method. The model’s performance is evaluated using three real-world count datasets, with goodness-of-fit assessed through the Kolmogorov–Smirnov (KS) test for discrete distributions, AIC, and BIC. The empirical results demonstrate that the NB-QX distribution outperforms Poisson, negative binomial, and negative binomial-gamma distributions, particularly in capturing overdispersion within a unified framework.

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