Banca de QUALIFICAÇÃO: ELISANGELA CANDEIAS BIAZATTI

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : ELISANGELA CANDEIAS BIAZATTI
DATE: 06/02/2023
LOCAL: Remoto
TITLE:

Some new distributions and new distributions families: Theory and applications

KEY WORDS:

COVID-19. Regression model. Dagum distribution. Beta Prime. Beta-G family.
Kumaraswamy-G family. Simulation.

PAGES: 84
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

In this work we propose a new generalization method from the Dagum distribution, called Dual-Dagum-G (DDa-G) with two parameters (DDa-G($a,b$)), and a new distribution called Weibull-Beta Prime with four parameters (WBP($a,b,\alpha,\beta$)). The first method obtained gains in the forms of the failure rate function, which, in addition to modeling data where the failure rate function has a decreasing and increasing shape, models inverted bathtub and bathtub shape. The new distribution generalizes the Beta Prime distribution, which considers two new parameters $a$ and $b$ and obtained a gain in modeling bimodal data, in addition to modeling data where the failure rate function has an increasing and inverted bathtub, decreasing and U shape. We propose the Log-Dual-Dagum-Weibull regression model (LDDa-W($a,b,\mu,\sigma$)) for the variable $Y=\log(X)$ where $X\sim\mbox{DDa-W}(a,b ,k,\lambda)$, with reparametrization $\lambda=\exp(\mu)$ and $k=1/\sigma$. In the case of the Weibull-Beta Prime regression model, the location and scale class was not used, a reparameterization of the parameter $\alpha$, i. e. the systematic component $\alpha_{i}=\exp(\vn_{i}^{\top}\lamn)$ was used. Properties such as quantile function, linear representation and moments are presented for the proposed family and distribution and the maximum likelihood method is used to estimate the parameters of the proposed models. Simulation studies are also performed both for a special case of the new family and for the new distribution. Finally, COVID-19 data sets were used to exemplify the gain of the new family and the new distribution in relation to other competitors. Studies were also carried out with the presence of covariates, the first set of data refers to the time (in days) elapsed from the date of hospitalization to death from the coronavirus, of 1,951 patients in Curitiba-PR, this study showed the superiority of the LDDa-W model. The second set of data refers to the time (in days) from the first symptom to death from COVID-19 of 655 patients in Campinas-SP, this study considered deaths from other causes or end of observation time as censoring and showed the superiority of the WBP model.

COMMITTEE MEMBERS:
Interno - 2937900 - ABRAAO DAVID COSTA DO NASCIMENTO
Presidente - 8383931 - GAUSS MOUTINHO CORDEIRO
Interna - 2991947 - MARIA DO CARMO SOARES DE LIMA