The Kumaraswamy Marshal-Olkin family of distributions | ||||
Journal of the Egyptian Mathematical Society | ||||
Volume 23, Issue 3, 2015, Page 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 | ||||
Statistics Article View: 57 PDF Download: 111 |
||||