Tbilisi Mathematical Journal

On Marshall-Olkin Burr X family of distribution

Farrukh Jamal, M. H. Tahir, Morad Alizadeh, and M. A. Nasir

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Generalizing distributions is important for applied statisticians and recent literature has suggested several ways of extending well-known distributions. We propose a new class of distributions called the Marshall-Olkin Burr X family, which yields exible shapes for its density such as symmetrical, left-skewed, right-skewed and reversed-J shaped, and can have increasing, decreasing,constant, bathtub and upside-down bathtub hazard rates shaped. Some of its structural properties including quantile and generating functions, ordinary and incomplete moments, and mean deviations are obtained. One special model of this family, the Marshall-Olkin-Burr-Lomax distribution, is investigated in details. We also derive the density of the order statistics. The model parameters are estimated by the maximum likelihood method. For illustrative purposes, three applications to real life data are presented.

Article information

Tbilisi Math. J., Volume 10, Issue 4 (2017), 175-199.

Received: 19 March 2017
Accepted: 10 May 2017
First available in Project Euclid: 21 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 62E10: Characterization and structure theory 62P10: Applications to biology and medical sciences

Marshall-Olkin distribution quantile function order statistics maximum likelihood estimation


Jamal, Farrukh; Tahir, M. H.; Alizadeh, Morad; Nasir, M. A. On Marshall-Olkin Burr X family of distribution. Tbilisi Math. J. 10 (2017), no. 4, 175--199. doi:10.1515/tmj-2017-0055. https://projecteuclid.org/euclid.tbilisi/1524276067

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