Flexible model for varying levels of zeros and outliers in count data

Touqeer Ahmad; Abid Hussain

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arXiv · 2510.27365

Flexible model for varying levels of zeros and outliers in count data

Touqeer Ahmad·Abid Hussain

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Abstract

Count regression models are necessary for examining discrete dependent variables alongside covariates. Nonetheless, when data display outliers, overdispersion, and an abundance of zeros, traditional methods like the zero-inflated negative binomial (ZINB) model sometimes do not yield a satisfactory fit, especially in the tail regions. This research presents a versatile, heavy-tailed discrete model as a resilient substitute for the ZINB model. The suggested framework is built by extending the generalized Pareto distribution and its zero-inflated version to the discrete domain. This formulation efficiently addresses both overdispersion and zero inflation, providing increased flexibility for heavy-tailed count data. Through intensive simulation studies and real-world implementations, the proposed models are thoroughly tested to see how well they work. The results show that our models always do better than classic negative binomial and zero-inflated negative binomial regressions when it comes to goodness-of-fit. This is especially true for datasets with a lot of zeros and outliers. These results highlight the proposed framework's potential as a strong and flexible option for modeling complicated count data.

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Touqeer Ahmad, Abid Hussain. 2025-10-31. Flexible model for varying levels of zeros and outliers in count data. https://arxiv.org/abs/2510.27365

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