The Kumaraswamy Marshal-Olkin family of distributions
Alizadeh, M., Tahir, M., Cordeiro, G., Mansoor, M., Zubair, M., Hamedani, G. (2015). The Kumaraswamy Marshal-Olkin family of distributions. EKB Journal Management System, 23(3), 546-557. doi: 10.1016/j.joems.2014.12.002
Morad Alizadeh; M.H. Tahir; Gauss M. Cordeiro; M. Mansoor; M. Zubair; G.G. Hamedani. "The Kumaraswamy Marshal-Olkin family of distributions". EKB Journal Management System, 23, 3, 2015, 546-557. doi: 10.1016/j.joems.2014.12.002
Alizadeh, M., Tahir, M., Cordeiro, G., Mansoor, M., Zubair, M., Hamedani, G. (2015). 'The Kumaraswamy Marshal-Olkin family of distributions', EKB Journal Management System, 23(3), pp. 546-557. doi: 10.1016/j.joems.2014.12.002
Alizadeh, M., Tahir, M., Cordeiro, G., Mansoor, M., Zubair, M., Hamedani, G. The Kumaraswamy Marshal-Olkin family of distributions. EKB Journal Management System, 2015; 23(3): 546-557. doi: 10.1016/j.joems.2014.12.002

The Kumaraswamy Marshal-Olkin family of distributions

Journal of the Egyptian Mathematical Society
Volume 23, Issue 3, 2015, Pages 546-557    PDF (733.08 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.12.002
Authors
Morad Alizadeh1; M.H. Tahir* 2; Gauss M. Cordeiro3; M. Mansoor2; M. Zubair4; G.G. Hamedani5
1Department of Statistics, Ferdowsi University of Mashhad, Mashhad, P.O. Box. 91775-1159, Iran
2Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
3Department of Statistics, Federal University of Pernambuco, 50740-540 Recife, PE, Brazil
4Department of Statistics, Government Degree College Khairpur Tamewali, Pakistan
5Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, USA
Abstract
We introduce a new family of continuous distributions called the Kumaraswamy
Marshal-Olkin generalized family of distributions. We study some mathematical properties of this
family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and
has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We
present some special models and investigate the asymptotics and shapes of the family. We derive
a power series for the quantile function and obtain explicit expressions for the moments, generating
function, mean deviations, two types of entropies and order statistics. Some useful characterizations
of the family are also proposed. The method of maximum likelihood is used to estimate the model
parameters. We illustrate the importance of the family by means of two applications to real data sets. 
Keywords
KEYWORDS Characterization; Estimation; Fre´chet distribution; Kumaraswamy distribution; Marshall-Olkin family; Weibull distribution
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