An alternative to the Cauchy distribution

Ayman Alzaatreh

doi:10.1016/j.mex.2019.02.025

An alternative to the Cauchy distribution

Ayman Alzaatreh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

A few generalizations of the Cauchy distribution appear in the literature. In this paper, a new generalization of the Cauchy distribution is proposed, namely, the exponentiated-exponential Cauchy distribution (EECD). Unlike the Cauchy distribution, EECD can have moments for some restricted parameters space. The distribution has wide range of skewness and kurtosis values and has a closed form cumulative distribution function. It can be left skewed, right skewed and symmetric. Two different estimation methods for the EECD parameters are studied. • A new generalization of the Cauchy distribution is proposed, namely, exponentiated-exponential Cauchy distribution (EECD). • EECD has flexible shape characteristics. Moreover, EECD moments are defined under some restrictions on the parameter space.

Original language	English
Pages (from-to)	938-952
Number of pages	15
Journal	MethodsX
Volume	6
DOIs	https://doi.org/10.1016/j.mex.2019.02.025
Publication status	Published - 2019

Keywords

Cauchy distribution
Estimation
Exponentiated-exponential-X family
Moments
Shannon entropy
T-X family

ASJC Scopus subject areas

Clinical Biochemistry
Medical Laboratory Technology

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title = "An alternative to the Cauchy distribution",

abstract = "A few generalizations of the Cauchy distribution appear in the literature. In this paper, a new generalization of the Cauchy distribution is proposed, namely, the exponentiated-exponential Cauchy distribution (EECD). Unlike the Cauchy distribution, EECD can have moments for some restricted parameters space. The distribution has wide range of skewness and kurtosis values and has a closed form cumulative distribution function. It can be left skewed, right skewed and symmetric. Two different estimation methods for the EECD parameters are studied. • A new generalization of the Cauchy distribution is proposed, namely, exponentiated-exponential Cauchy distribution (EECD). • EECD has flexible shape characteristics. Moreover, EECD moments are defined under some restrictions on the parameter space.",

keywords = "Cauchy distribution, Estimation, Exponentiated-exponential-X family, Moments, Shannon entropy, T-X family",

author = "Ayman Alzaatreh",

note = "Funding Information: The author is grateful to the Editor and the reviewers for their comments and suggestions that have greatly improved the paper. The author gratefully acknowledge the support of the American University of Sharjah . Publisher Copyright: {\textcopyright} 2019 The Author(s)",

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doi = "10.1016/j.mex.2019.02.025",

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volume = "6",

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T1 - An alternative to the Cauchy distribution

AU - Alzaatreh, Ayman

N1 - Funding Information: The author is grateful to the Editor and the reviewers for their comments and suggestions that have greatly improved the paper. The author gratefully acknowledge the support of the American University of Sharjah . Publisher Copyright: © 2019 The Author(s)

PY - 2019

Y1 - 2019

N2 - A few generalizations of the Cauchy distribution appear in the literature. In this paper, a new generalization of the Cauchy distribution is proposed, namely, the exponentiated-exponential Cauchy distribution (EECD). Unlike the Cauchy distribution, EECD can have moments for some restricted parameters space. The distribution has wide range of skewness and kurtosis values and has a closed form cumulative distribution function. It can be left skewed, right skewed and symmetric. Two different estimation methods for the EECD parameters are studied. • A new generalization of the Cauchy distribution is proposed, namely, exponentiated-exponential Cauchy distribution (EECD). • EECD has flexible shape characteristics. Moreover, EECD moments are defined under some restrictions on the parameter space.

AB - A few generalizations of the Cauchy distribution appear in the literature. In this paper, a new generalization of the Cauchy distribution is proposed, namely, the exponentiated-exponential Cauchy distribution (EECD). Unlike the Cauchy distribution, EECD can have moments for some restricted parameters space. The distribution has wide range of skewness and kurtosis values and has a closed form cumulative distribution function. It can be left skewed, right skewed and symmetric. Two different estimation methods for the EECD parameters are studied. • A new generalization of the Cauchy distribution is proposed, namely, exponentiated-exponential Cauchy distribution (EECD). • EECD has flexible shape characteristics. Moreover, EECD moments are defined under some restrictions on the parameter space.

KW - Cauchy distribution

KW - Estimation

KW - Exponentiated-exponential-X family

KW - Moments

KW - Shannon entropy

KW - T-X family

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JO - MethodsX

JF - MethodsX

SN - 2215-0161

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An alternative to the Cauchy distribution

Abstract

Keywords

ASJC Scopus subject areas

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