New flexible versions of extended generalized Pareto model for count data

TL;DR

This paper introduces new flexible extended generalized Pareto models for count data that effectively model entire distributions, zero-inflation, and tail behavior without strict threshold selection, outperforming existing models.

Contribution

The paper proposes novel extended DGPD models capable of modeling full data, zero-inflation, and low-threshold exceedances, addressing limitations of existing distributions.

Findings

Extended models outperform existing models in simulations.

Models accurately capture tail and bulk of data.

Real data applications show improved estimation.

Abstract

Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants, are considered suitable for modeling the entire data distribution, but they fail to capture the heavy tail behavior effectively alongside the bulk of the distribution. In contrast, the discrete generalized Pareto distribution (DGPD) is preferred for high threshold exceedances, but it becomes less effective for low threshold exceedances. However, in some applications, the selection of a suitable high threshold is challenging, and the asymptotic conditions required for using DGPD are not always met. To address these limitations, extended versions of DGPD are proposed. These extensions are designed to model one of three scenarios: first, the entire distribution of the data, including both bulk and tail and bypassing the threshold selection step; second, the entire distribution along with ZI; and third, the tail of the distribution for low threshold exceedances. The proposed extensions offer improved estimates across all three scenarios compared to existing models, providing more accurate and reliable results in simulation studies and real data applications.