The generalized Cauchy family of distributions with applications

Ayman Alzaatreh, Carl Lee, Felix Famoye, Indranil Ghosh

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

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.

Original languageEnglish
Article number12
JournalJournal of Statistical Distributions and Applications
Volume3
Issue number1
DOIs
StatePublished - Dec 1 2015

Keywords

  • Moments
  • Quantile function
  • Shannon’s entropy
  • T-R{Y} framework

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