The generalized Cauchy family of distributions with applications

Ayman Yousef Abdelfattah Alzaatreh, Carl Lee, Felix Famoye, Indranil Ghosh

Research output: Contribution to journalArticle

2 Citations (Scopus)

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
Publication statusPublished - Dec 1 2015

Fingerprint

Cauchy
Logistics
Cauchy Distribution
Entropy
Quantile Function
Mean deviation
Extreme Values
Exponential distribution
Family
Moment

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computer Science Applications

Cite this

The generalized Cauchy family of distributions with applications. / Yousef Abdelfattah Alzaatreh, Ayman; Lee, Carl; Famoye, Felix; Ghosh, Indranil.

In: Journal of Statistical Distributions and Applications, Vol. 3, No. 1, 12, 01.12.2015.

Research output: Contribution to journalArticle

@article{d3e6766e6ad640f08bd7589c58fd0c84,
title = "The generalized Cauchy family of distributions with applications",
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 Fr{\'e}chet 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.",
keywords = "Moments, Quantile function, Shannon’s entropy, T-R{Y} framework",
author = "{Yousef Abdelfattah Alzaatreh}, Ayman and Carl Lee and Felix Famoye and Indranil Ghosh",
year = "2015",
month = "12",
day = "1",
doi = "10.1186/s40488-016-0050-3",
language = "English",
volume = "3",
journal = "Journal of Statistical Distributions and Applications",
issn = "2195-5832",
publisher = "Springer Open",
number = "1",

}

TY - JOUR

T1 - The generalized Cauchy family of distributions with applications

AU - Yousef Abdelfattah Alzaatreh, Ayman

AU - Lee, Carl

AU - Famoye, Felix

AU - Ghosh, Indranil

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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.

AB - 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.

KW - Moments

KW - Quantile function

KW - Shannon’s entropy

KW - T-R{Y} framework

UR - http://www.scopus.com/inward/record.url?scp=85053018441&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053018441&partnerID=8YFLogxK

U2 - 10.1186/s40488-016-0050-3

DO - 10.1186/s40488-016-0050-3

M3 - Article

VL - 3

JO - Journal of Statistical Distributions and Applications

JF - Journal of Statistical Distributions and Applications

SN - 2195-5832

IS - 1

M1 - 12

ER -