The Exponentiated Power Generalized Weibull: Properties and Applications

• Main Authors: FERNANDO A. PEÑA-RAMÍREZ, RENATA R. GUERRA, GAUSS M. CORDEIRO, PEDRO R.D. MARINHO
• Format: Article
• Language: English
• Published: Academia Brasileira de Ciências
• Series: Anais da Academia Brasileira de Ciências
• Subjects: Exponential distribution; lifetime data; Nadarajah-Haghighi distribution; power generalized Weibull distribution; survival function
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652018000602553&lng=en&tlng=en

Abstract We propose a new lifetime model called the exponentiated power generalized Weibull (EPGW) distribution, which is obtained from the exponentiated family applied to the power generalized Weibull (PGW) distribution. It can also be derived from a power transform on an exponentiated Nadarajah-Haghighi random variable. Since several structural properties of the PGW distribution have not been studied, they can be obtained from those of the EPGW distribution. The model is very flexible for modeling all common types of hazard rate functions. It is a very competitive model to the well-known Weibull, exponentiated exponential and exponentiated Weibull distributions, among others. We also give a physical motivation for the new distribution if the power parameter is an integer. Some of its mathematical properties are investigated. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters.