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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Abstract

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

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

Dates
Received: 13 September 2017
Accepted: 21 December 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276031

Digital Object Identifier
doi:10.2478/tmj-2018-0005

Mathematical Reviews number (MathSciNet)
MR3767423

Zentralblatt MATH identifier
06856988

Subjects
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.)

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

Citation

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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