Kumaraswamy Distribution Based on Alpha Power Transformation Methods
H. E. Hozaien
Department of Statistics, Faculty of Commerce, AL-Azhar University, (Girls’ Branch), Cairo, Egypt.
G. R. AL Dayian
Department of Statistics, Faculty of Commerce, AL-Azhar University, (Girls’ Branch), Cairo, Egypt.
A. A. EL-Helbawy *
Department of Statistics, Faculty of Commerce, AL-Azhar University, (Girls’ Branch), Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.
Keywords: Alpha power transformation, new alpha power transformed, new extended alpha power transformed, Kumaraswamy distribution, maximum likelihood estimation.