A New Extended Weibull Distribution with Application to Influenza and Hepatitis Data

Gauss M. Cordeiro (), Elisângela C. Biazatti and Luís H. de Santana
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Gauss M. Cordeiro: Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil
Elisângela C. Biazatti: Department of Mathematics and Statistics, Federal University of Rondônia, Ji-Paraná 76900-726, Brazil
Luís H. de Santana: Department of Technology, State University of Maringá, Umuarama 87506-370, Brazil

Stats, 2023, vol. 6, issue 2, 1-17

Abstract: The Weibull is a popular distribution that models monotonous failure rate data. In this work, we introduce the four-parameter Weibull extended Weibull distribution that presents greater flexibility, thus modeling data with bathtub-shaped and unimodal failure rate. Some of its mathematical properties such as quantile function, linear representation and moments are provided. The maximum likelihood estimation is adopted to estimate its parameters, and the log-Weibull extended Weibull regression model is presented. In addition, some simulations are carried out to show the consistency of the estimators. We prove the greater flexibility and performance of this distribution and the regression model through applications to influenza and hepatitis data. The new models perform much better than some of their competitors.

Keywords: maximum likelihood estimation; moment; Monte Carlo simulation; regression; Weibull-G class (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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