A new extended alpha power transformed family of distributions: properties and applications

Document Type: Original Scientific Paper


1 Department of Statistics, Quaid-i-Azam University 45320, Islamabad, Pakistan

2 Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSA

3 Department of Statistics, Government Postgraduate College Jhang, Pakistan


In this paper, a new method has been proposed to introduce an extra parameter to a family of lifetime distributions for more flexibility. A special sub-case has been considered in details namely; two parameters Weibull distribution. Various mathematical properties of the proposed distribution, including explicit expressions for the moments, quantile, moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study is conducted to evaluate the performances of these estimators. For the illustrative purposes, two data sets have
been analyzed to show how the proposed model work in practice.