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 | |
| Publication status | Published - Jan 1 2019 |
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Keywords
- Cauchy distribution
- Estimation
- Exponentiated-exponential-X family
- Moments
- Shannon entropy
- T-X family
ASJC Scopus subject areas
- Clinical Biochemistry
- Medical Laboratory Technology
Cite this
An alternative to the Cauchy distribution. / Yousef Abdelfattah Alzaatreh, Ayman.
In: MethodsX, Vol. 6, 01.01.2019, p. 938-952.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An alternative to the Cauchy distribution
AU - Yousef Abdelfattah Alzaatreh, Ayman
PY - 2019/1/1
Y1 - 2019/1/1
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
UR - http://www.scopus.com/inward/record.url?scp=85064879651&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85064879651&partnerID=8YFLogxK
U2 - 10.1016/j.mex.2019.02.025
DO - 10.1016/j.mex.2019.02.025
M3 - Article
AN - SCOPUS:85064879651
VL - 6
SP - 938
EP - 952
JO - MethodsX
JF - MethodsX
SN - 2215-0161
ER -