Banca de DEFESA: FELIPE FERNANDO ANGELO BARRETO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : FELIPE FERNANDO ANGELO BARRETO
DATE: 28/02/2024
TIME: 14:00
LOCAL: meet.google.com/cuu-ikmj-bqm
TITLE:

Generalized transmuted families: some information and Goodness-of-fit measures based on the Mellin transform

KEY WORDS:

Generalized transmuted families; Mellin Transform, Goodness-of-Fit Measures, Information measures, Hotelling Statistics.

PAGES: 82
BIG AREA: Ciências Agrárias
AREA: Agronomia
SUMMARY:

Probability distribution models have been widely studied by researchers and scientists for describing and explaining natural phenomena. In recent years, several more flexible probability distribution models have been proposed to describe data, for example in Survival Analysis. Among the models proposed in the literature, Generalized Transmuted Families stand out as they are efficient in describing and explaining data of this nature. Despite many published works that deal with new models or classes of distributions, few are aimed at developing efficient goodness-of-fit measures. The objectives of this work are: (i) to propose a new estimation criterion and goodness-of-fit measures - considering qualitative and quantitative aspects - based on the Mellin Transform. Such goodness-of-fit measures were developed using Hotelling statistics and applied, initially, to four submodels of the Transmuted-G class: Transmuted Weibull, Transmuted Fréchet, Transmuted log-logistics and Transmuted Pareto; and, later, in two submodels of the New Transmutada-G class: New Transmutada Weibull and New Transmutada Fréchet. To verify the performance of the proposed methodology, a survival analysis database and SAR image data were used; (ii) Explore properties relating to information measurements for the New Transmuted-G class: Shannon Entropy; Fisher information and mean Gini divergence. Furthermore, divergence measures such as Kullback-Leibler divergence and Chi-Square divergence were obtained to measure the closeness between two probability distributions. The density of Nova Transmutada-G is written as a mixture between the base distribution and the exponentiated base distribution, which are called its components. Furthermore, divergence measures, such as Kullback-Leibler and Chi-Square, were obtained to measure the proximity between two probability distributions within such a class, that is, between the generator's density function and its components. It was found that the Kullback-Leibler divergence between a New Transmuted-G model and its components is free from the base distribution. Furthermore, the mean Gini difference is expressed as the sum of the mean Gini difference of its components.

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