Zubair Ahmad - Department of Statistics, Quaid-i-Azam University ۴۵۳۲۰, Islamabad, Pakistan
M. Elgarhy - Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSA
Nasir Abbas - 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 havebeen analyzed to show how the proposed model work in practice.

Alpha power transformation, Family of distributions, Maximum likelihood estimation, Moments, Order statistic, Residual life function, Weibull distribution