Equidispersion in Count Data: A Comparative Study of Zero-Modified Distributions

• Grant number: 25/14961-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2025
• End date: September 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Katiane Silva Conceição
• Grantee: Antonio Augusto Nunes de Souza
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This work aims to evaluate the performance of a more flexible distribution (the Zero-Modified Negative Binomial Distribution) in scenarios where a simpler distribution, such as the Zero-Modified Poisson Distribution, is theoretically appropriate. Specifically, it seeks to investigate the performance of the Zero-Modified Negative Binomial in equidispersed dataset, that is, those originating from populations in which the mean and variance are equal. To this end, a comparative study will be conducted to assess the quality of the fits provided by both distributions, based on parameter estimation through the maximum likelihood method. The selection of the distribution that best fits a given dataset will be based on evidence measures such as the Euclidean distance and the Kullback-Leibler divergence, as well as complementary graphical analyses. In addition, a simulation study will be carried out in order to compare the adequacy of the fitted models under different conditions, and real data applications will be presented to illustrate the results obtained.