TY - JOUR
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 .
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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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 -