The generalized Cauchy family of distributions with applications

Ayman Alzaatreh, Carl Lee, Felix Famoye, Indranil Ghosh
2016 Journal of Statistical Distributions and Applications  
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}
more » ... ibution, 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.
doi:10.1186/s40488-016-0050-3 fatcat:wev5rpu3ejavldl7dfho56pyfq