Banca de DEFESA: LETÍCIA SOUZA DE OLIVEIRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LETÍCIA SOUZA DE OLIVEIRA
DATE: 28/02/2025
TIME: 14:00
LOCAL: https://meet.google.com/tgc-fqdc-nib
TITLE:

Modelo $\Gamma$-G; Índice de Gini; Métodos computacionais; Métodos de estimação; Desigualdade de renda; Estudos numéricos.

KEY WORDS:

$\Gamma$-G model; Gini index; Computational methods; Estimation methods; Income inequality; Numerical studies.

PAGES: 62
BIG AREA: Ciências Agrárias
AREA: Agronomia
SUMMARY:

This work presents the development of a new three-parameter probabilistic model, named $\Gamma$-MK, designed to model data restricted to the unit interval, such as rates and proportions. The model combines the gamma-G generator with the Modified Kumaraswamy distribution, offering greater flexibility and accuracy in data analysis within this interval. The primary motivation is the need for more adaptable models to describe various phenomena. The proposed model stands out for its high flexibility and computational simplicity, with all mathematical expressions efficiently treatable, facilitating its practical application in different contexts. Simulation studies were conducted using five estimation methods: maximum likelihood, least squares, maximum product spacing, Anderson–Darling, and Cramér–von Mises. The results indicated that the estimates exhibited consistent behavior across methods, with biases decreasing as sample size increased, demonstrating the model's robustness and feasibility for practical applications. An application to real-world data was performed using the Gini index of 61 countries, analyzed in a cross-sectional format for the period from 2005 to 2019. To handle missing data, the supervised machine learning method \textit{K-Nearest Neighbors} was employed, preserving the empirical distribution of the original data. The descriptive analysis revealed stability in inequality indices over the years, while the $\Gamma$-MK model adjustments showed superior performance compared to classical distributions, such as beta and Kumaraswamy, in $87\%$ of the evaluated scenarios. Goodness-of-fit metrics, such as Akaike Information Criterion, Bayesian Information Criterion, Corrected Akaike Information Criterion, Kolmogorov-Smirnov, Anderson–Darling, and Cramér–von Mises, corroborated the superiority of the proposed model. Additionally, we present mathematical properties of the proposed model, including density expansion, quantile function, ordinary moments, skewness, kurtosis, reliability, and entropy. The model's flexibility allows capturing different patterns of skewness and kurtosis, making it particularly useful for economic data and variables restricted to the unit interval. The analysis of the Lorenz curve and the Gini index further reinforced the model's potential to assess income inequalities.

COMMITTEE MEMBERS:
Externo à Instituição - FIDEL ERNESTO CASTRO MORAES - UFRJ
Presidente - FRANK SINATRA GOMES DA SILVA
Externo à Instituição - THIAGO ALEXANDRO NASCIMENTO DE ANDRADE - UFSM