Banca de QUALIFICAÇÃO: MARÍLIA GABRIELA FERREIRA DE MIRANDA OLIVEIRA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : MARÍLIA GABRIELA FERREIRA DE MIRANDA OLIVEIRA
DATE: 30/08/2024
TIME: 14:00
LOCAL: https://meet.google.com/hys-wauu-rvf
TITLE:

Mellin-type statistics for the Cubic Transmuted Class and bias correction for the q-Exponential model

KEY WORDS:

Log-cumulants method. Method of moments. Mellin Transform. Log-cumulant diagram. Bias correction.

PAGES: 59
BIG AREA: Ciências Agrárias
AREA: Agronomia
SUMMARY:

Probability models are mathematical structures that represent uncertainty and describe random phenomena. These models are widely used to make predictions, make decisions, and understand data variability. Examples of applications include areas such as medicine, reliability, and engineering. In addition to practical applications, probability models help predict behaviors of real data, minimize risks, and test hypotheses. New probability models are constantly emerging in the literature, such as the Marshall-Olkin Class, Lindley distribution, q-distributions, Slashed-Lomax model, G-Normal Class, among others. For a probability model to be validated, it must fit the data well. Once the model is well specified, its parameters need to be estimated, a crucial step to make distributions more accurate and allow for more reliable inferences. Despite the variety of new models in the literature, there is often a lack of sufficient tools to effectively assess their goodness of fit. Therefore, the objectives of this work are: (i) To introduce new goodness-of-fit measures for some models of the Cubic Transmuted (CT) class: CT-Weibull, CT-Logistic and CT-Fréchet. These new measures are mainly based on the log-cumulant methodology (second-type statistics), obtained through the Mellin Transform (MT). We present a theorem that illustrates the MT for any submodel of the CT class, produce a two-dimensional and three-dimensional log-cumulant diagram as a visual graphical tool to select models of this class, and a hypothesis test based on Hotelling's T² Statistic. Applications in the area of survival analysis are made to illustrate the developed tools, considering qualitative and quantitative aspects. (ii) To explore the bias correction of maximum likelihood estimators of the q-Exponential model, using the Cox-Snell method, which is based on the calculation of the expectations of the second and third derivatives of the log-likelihood function; the Firth method, which performs estimation and correction simultaneously; and the resampling method, parametric Bootstrap. To explore the correction, a Monte Carlo Simulation was performed considering the bias assessment metrics and root mean square error. The partial simulation results show that the corrections are efficient for small samples, with Cox-Snell being the most effective method for correcting maximum likelihood estimators.

COMMITTEE MEMBERS:
Presidente - FRANK SINATRA GOMES DA SILVA
Interno - JADER DA SILVA JALE
Interno - JOSIMAR MENDES DE VASCONCELOS
Externo à Instituição - RENILMA PEREIRA DA SILVA - UFRN
Externo à Instituição - THIAGO ALEXANDRO NASCIMENTO DE ANDRADE - UFSM