A new alpha power transformed family of distributions: properties and applications to the Weibull model

Volume 12, Issue 1, pp 1--20 http://dx.doi.org/10.22436/jnsa.012.01.01 Publication Date: September 28, 2018       Article History


I. Elbatal - Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University, (IMSIU), Saudi Arabia. Zubair Ahmad - Department of Statistics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan. M. Elgarhy - Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSA. Abdullah M. Almarashi - Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah, Kingdom of Saudi Arabia.


In this article, a new technique of alpha-power transformation is used to propose a new class of lifetime distributions. Four special models of the new family are presented. Some mathematical properties of the proposed model including estimation of the unknown parameters using the method of maximum likelihood are discussed. For the illustrative purposes of the new proposal, a three-parameter special model of this class, namely, new alpha-power transformed Weibull distribution is considered in detail. The proposed distribution offers greater distributional flexibility and is able to model data with increasing, decreasing, and constant or more importantly with bathtub-shaped failure rates. Type-1 and Type-II censoring estimation are discussed. A simulation study based on complete sample of the new model is also carried out. Finally, the usefulness and efficiency of the new proposal is illustrated by analyzing two real data sets.