The transmuted transmuted-G family: properties and applications

Volume 12, Issue 4, pp 217--229 http://dx.doi.org/10.22436/jnsa.012.04.03 Publication Date: December 05, 2018       Article History

Authors

M. M. Mansour - Department of MIS, Yanbu, Taibah University, Saudi Arabia. - Department of Statistics, Mathematics and Insurance, Benha University, Egypt. Enayat M. Abd Elrazik - Department of MIS, Yanbu, Taibah University, Saudi Arabia. - Department of Statistics, Mathematics and Insurance, Benha University, Egypt. Ahmed Z. Afify - Department of Statistics, Mathematics and Insurance, Benha University, Egypt. Mohammad Ahsanullah - Department of Management Sciences, Rider University NJ, USA. Emrah Altun - Department of Statistics, Bartin University, Bartin 74100, Turkey.


Abstract

This paper introduces a new family of continuous distributions called the transmuted transmuted-G family which extends the quadratic rank transmutation map pioneered by Shaw and Buckley [W. T. Shaw, I. R. Buckley, arXiv preprint, \(\textbf{2007}\) (2007), 28 pages]. We provide two special models of the new family which can be used effectively to model survival data since they accommodate increasing, decreasing, unimodal, bathtub-shaped and increasing-decreasing-increasing hazard functions. We also provide two new characterization theorems of the proposed family. The estimation of the model parameters is performed by the maximum likelihood method. The flexibility of the proposed family is illustrated by means of two applications to real data.


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