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Revista Colombiana de Estadística

versão impressa ISSN 0120-1751

Rev.Colomb.Estad. vol.46 no.2 Bogotá jul./dez. 2023  Epub 02-Jul-2023

https://doi.org/10.15446/rce.v46n2.103412 

Original articles of research

A New Nadarajah-Haghighi Generalization with Five Different Shapes for the Hazard Function

Una nueva generalización de la distribución Nadarajah-Haghighi con cinco formas diferentes de función de hazard

Fernando A. Peña-Ramírez1  a 

Renata Rojas Guerra2  b 

Gauss M. Cordeiro3  c 

1Department of Statistics, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia

2Department of Statistics, Centro de Ciências Naturais e Exatas, Universidade Federal de Santa Maria, Santa Maria, Brasil

3Department of Statistics, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco, Recife, Brasil


Abstract

We introduce a four-parameter model called the Weibull Nadarajah-Haghighi distribution. It is obtained by inserting the Nadarajah-Haghighi distribution in the Weibull-G family. The proposed distribution can produce constant, increasing, decreasing, bathtub, and upside down-bathtub hazard rate shapes, which are the most important in lifetime analysis. We explore some structural properties, including the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, and Rényi entropy. The maximum likelihood method is used to estimate the model parameters. A simulation study is formed to examine the precision of the estimates. The usefulness of the new distribution is illustrated through two applications to real data. The new model provides better fits than some widely known lifetime distributions.

Key words: Hazard rate function; Lifetime data; Maximum likelihood; Nadarajah-Haghighi distribution; Weibull-G family

Resumen

Este trabajo introduce un nuevo modelo probabilístico de cuatro parámetros llamado distribución Weibull Nadarajah-Haghighi. Este modelo es obtenido mediante la inserción de la distribución Nadarajah-Haghighi en la familia Weibull-G. Un punto destacado de esta nueva propuesta son sus formas en la función de hazard: constante, creciente, decreciente, bañera y bañera invertida, que son las más importantes en el análisis de supervivencia. En este trabajo también se exploran algunas propiedades estructurales del modelo, como la función cuantil, los momentos ordinarios e incompletos, las desviaciones medias, las curvas de Bonferroni y Lorenz y la entropía de Rényi. Para la estimación de los parámetros, se utiliza el método de máxima verosimilitud. Además, un estudio de simulación de Monte Carlo se realiza para examinar el desempeño de las estimaciones. La utilidad de la nueva distribución se ilustra a través del ajuste en dos conjuntos de datos reales. El nuevo modelo muestra mejores ajustes que algunas distribuciones consideradas canónicas en análisis de supervivencia.

Palabras clave: Distribución Nadarajah-Haghighi; Familia Weibull-G; Función de hazard; Máxima verosimilitud; Tiempos de sobrevida

Full text available only in PDF format

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Received: June 2022; Accepted: May 2023

aAssistant Professor. E-mail: fapenara@unal.edu.co

bAssistant Professor. E-mail: renata.r.guerra@ufsm.br

cFull Professor. E-mail: gauss@de.ufpe.br

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