Tbilisi Mathematical Journal

A new extended generalized Burr-III family of distributions

Farrukh Jamal, Mohammad A. Aljarrah, M. H. Tahir, and M. Arslan Nasir

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In this paper, we introduce a new extended generalized Burr III family of distributions in the so-called T-BurrIII{Y} family by using the quantile functions of a few popular distributions. We derive the general mathematical properties of this extended family including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Three new Burr III sub-families are then investigated, and four new extended Burr III models are discussed. The density of Burr III extended distributions can be symmetric, left-skewed, right-skewed or reversed-J shaped, and the hazard rate shapes can be increasing, decreasing, bathtub and upside-down bathtub. The potentiality of the newly generated distributions is demonstrated through applications to censored and complete data sets.

Article information

Tbilisi Math. J., Volume 11, Issue 1 (2018), 59-78.

Received: 13 September 2017
Accepted: 21 December 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 62H20: Measures of association (correlation, canonical correlation, etc.)

Burr III distribution generalization quantile function T-X family T-R{Y} family


Jamal, Farrukh; Aljarrah, Mohammad A.; Tahir, M. H.; Nasir, M. Arslan. A new extended generalized Burr-III family of distributions. Tbilisi Math. J. 11 (2018), no. 1, 59--78. doi:10.2478/tmj-2018-0005. https://projecteuclid.org/euclid.tbilisi/1524276031

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