Novel Discrete Composite Distributions with Applications to Infectious Disease Data

TL;DR

This paper introduces new discrete composite distributions with Pareto tails to better model infectious disease data, addressing limitations of traditional Pareto models and providing tools for statistical inference on tail behavior.

Contribution

The paper proposes novel discrete composite distributions with Pareto tails and develops hypothesis testing for tail index, improving modeling and inference for infectious disease data.

Findings

Discrete composite distributions outperform traditional models

Tail index testing offers insights into disease spread

Models fit COVID-19 and monkeypox data effectively

Abstract

It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths of infectious diseases, a major limitation of Pareto distribution is that it can only fit a given data set beyond a certain threshold. Thus, it can only model part of the data set. Thus, we proposed some novel discrete composite distributions with Pareto tails to fit the real infectious disease data. To provide necessary statistical inference for the tail behavior of the data, we developed a hypothesis testing procedure to test the tail index parameter. COVID-19 reported cases in Singapore and monkeypox reported cases in France were analyzed to evaluate the performance of the newly created distributions. The results from the analysis suggested that the discrete composite distributions could demonstrate competitive performance compared to the commonly used discrete distributions. Furthermore, the analysis of the tail index parameter can provide great insights into preventing and controlling infectious diseases.