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<p>This paper puts forward a new approach to modeling variables with unit interval values. More specifically, a three-parameter distribution (and model) with unit support is proposed which benefits from a high degree of flexibility to fit the data accurately. All the associated formulas are computationally tractable, allowing its practical application. Simulation studies were carried out using five different estimation methods, including the maximum likelihood and least squares methods. The behavior of the estimates was congruent for all methods, with biases decreasing as the sample size increases. These results show that the proposed model is feasible for practical applications, with inferential procedures easily obtained. A large data set on the Gini index of 61 countries was analyzed cross-sectionally from 2005 to 2019. Missing data were treated with the supervised machine learning method K-Nearest Neighbors without significantly changing the empirical distribution of the data. The results obtained in the application favor the proposed model over classical alternatives, such as the Beta and Kumaraswamy models, as well as a recent and promising extension known as the Exponentiated Kumaraswamy model.</p>

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Probabilistic Modeling and Supervised Machine Learning Technique in Gini Index Analysis: The New \(\Gamma \text {-}\text{MK}\) Model

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Thiago A. N. de Andrade,
  • Frank Gomes-Silva,
  • Christophe Chesneau,
  • Letícia Souza de Oliveira

摘要

This paper puts forward a new approach to modeling variables with unit interval values. More specifically, a three-parameter distribution (and model) with unit support is proposed which benefits from a high degree of flexibility to fit the data accurately. All the associated formulas are computationally tractable, allowing its practical application. Simulation studies were carried out using five different estimation methods, including the maximum likelihood and least squares methods. The behavior of the estimates was congruent for all methods, with biases decreasing as the sample size increases. These results show that the proposed model is feasible for practical applications, with inferential procedures easily obtained. A large data set on the Gini index of 61 countries was analyzed cross-sectionally from 2005 to 2019. Missing data were treated with the supervised machine learning method K-Nearest Neighbors without significantly changing the empirical distribution of the data. The results obtained in the application favor the proposed model over classical alternatives, such as the Beta and Kumaraswamy models, as well as a recent and promising extension known as the Exponentiated Kumaraswamy model.