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. JEL classification: C10, C13, C15, C46, Method name: The paper proposes an alternative to the Cauchy distribution using the T-X family framework proposed by Alzaatreh et al. (2013). The proposed distribution can be left skewed, right skewed or symmetric. The moments are defined under some restriction on the parameter space, Keywords: Estimation, Moments, T-X family, Exponentiated-exponential-X family, Shannon entropy, Cauchy distribution