The Weibull–Dagum distribution: Properties and applications. Issue 24 (16th December 2016)

• Record Type: Journal Article
• Authors: Tahir, M. H.; Cordeiro, Gauss M.; Mansoor, M.; Zubair, M.; Alizadeh, Morad
• Is Part Of: Communications in statistics. Volume 45:Issue 24(2016)
• Page Start: 7376
• Page End: 7398
• Publication Date: 2016-12-16
• Subjects: Dagum distribution -- Hazard function -- Likelihood estimation -- Moment -- Weibull-G family.; 60E05 -- 62F10 -- 62N05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.983610
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this article, we define a new lifetime model called the Weibull–Dagum distribution. The proposed model is based on the Weibull–G class. It can also be defined by a simple transformation of the Weibull random variable. Its density function is very flexible and can be symmetrical, left-skewed, right-skewed, and reversed-J shaped. It has constant, increasing, decreasing, upside-down bathtub, bathtub, and reversed-J shaped hazard rate. Various structural properties are derived including explicit expressions for the quantile function, ordinary and incomplete moments, and probability weighted moments. We also provide explicit expressions for the Rényi and q-entropies. We derive the density function of the order statistics as a mixture of Dagum densities. We use maximum likelihood to estimate the model parameters and illustrate the potentiality of the new model by means of a simulation study and two applications to real data. In fact, the proposed model outperforms the beta-Dagum, McDonald–Dagum, and Dagum models in these applications.