- Ayman AlzaatrehEmail author,
- Carl Lee,
- Felix Famoye and
- Indranil Ghosh
Journal of Statistical Distributions and Applications20163:12
DOI: 10.1186/s40488-016-0050-3
© The Author(s). 2016
[size=0.8125]Received: 23 February 2016
[size=0.8125]Accepted: 13 July 2016
[size=0.8125]Published: 3 August 2016
Abstract
A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entropy. Some members of the T-Cauchy{Y} family are developed and one member, gamma-Cauchy{exponential} distribution, is studied in detail. The distributions in the T-Cauchy{Y} family are very flexible due to their various shapes. The distributions can be symmetric, skewed to the right or skewed to the left.