A skewed truncated Cauchy distribution with applications in economics

Abstract

Skewed symmetric distributions have attracted a great deal of attention in the last few years. One of them, the skewed Cauchy distribution suffers from limited applicability because of the lack of finite moments. This article proposes an alternative to the skewed Cauchy distribution, which we refer to as skewed truncated Cauchy distribution. It is defined by the pdf f(x) = 2g(x)G(γx), where g(·) and G(·) are taken, respectively, to be the pdf and the cdf of a truncated Cauchy distribution. This distribution possesses finite moments of all orders and could therefore be a better model for certain practical situations. One such situation in economics is discussed. This article also derives various properties of this distribution, including its moments.