The Kumaraswamy Marshal-Olkin family of distributions

Alizadeh, Morad; Tahir, M.H.; Cordeiro, Gauss M.; Mansoor, M.; Zubair, M.; Hamedani, G.G.

doi:10.1016/j.joems.2014.12.002

The Kumaraswamy Marshal-Olkin family of distributions

Document Type : Original Article

Authors

¹ Department of Statistics, Ferdowsi University of Mashhad, Mashhad, P.O. Box. 91775-1159, Iran

² Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

³ Department of Statistics, Federal University of Pernambuco, 50740-540 Recife, PE, Brazil

⁴ Department of Statistics, Government Degree College Khairpur Tamewali, Pakistan

⁵ Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, USA

10.1016/j.joems.2014.12.002

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