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

TL;DR

This paper introduces a flexible, heavy-tailed discrete model based on the generalized Pareto distribution to better handle count data with zeros, outliers, and overdispersion, outperforming traditional models.

Contribution

The paper develops a new discrete heavy-tailed model extending the generalized Pareto distribution, offering improved fit for complex count data with zeros and outliers.

Findings

Proposed models outperform negative binomial in goodness-of-fit.

Models effectively handle zero inflation and overdispersion.

Simulation and real data validate model robustness.

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.