A New Family of Distributions in the Class of the Alpha Power Transformation with Applications to Income
R. M. Mandouh *
Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
E. M. Sewilam
Department of Statistics, Faculty of Commerce, AL-Azhar University, (Girls' Branch), Cairo, Egypt.
M. M. Abdel-Zaher
Department of Statistics, Faculty of Commerce, AL-Azhar University, (Girls' Branch), Cairo, Egypt.
M. R. Mahmoud
Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new technique of the alpha-power transformation (APT) is used to propose a new class of probability distribution which is particularly useful for analysis of lifetime data. For the illustrative purposes of the new proposal, a special sub-model of the proposed family is considered in details. Various mathematical properties of the proposed model including quantile function, moments and moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood method is used to estimate the unknown parameters. Finally A real data set is analyzed using the new distribution, and a simulation study is carried out to asses the performance of the new family.
Keywords: Alpha power transformation, Dagum distribution, moment generating function, maximum likelihood estimation, Gini coefficient.