Asymmetric Parametric Distributions and a New Class of Asymmetric Generalized t-Distribution

Abstract

This paper describes a general procedure for constructing a class of asymmetric distributions based on symmetric parametric distribution families, and investigates some inherent relationships between the constructed asymmetric distribution and the original symmetric ones. This procedure is used to construct an asymmetric generalized t (AGT) distribution that nests many commonly used distributions such as the skewed generalized t (GT), generalized error distribution (GED), Student t and Normal distributions. We investigate properties of the new distribution, give procedures for estimation, and derive analytical expressions for the cdf, quantile function, moments, Renyi entropy. Although the AGT density does not satisfy the usual regularity conditions for maximum likelihood estimation, we establish consistency, asymptotic normality and efficiency of ML estimators and derive an explicit analytical expression for the asymptotic covariance matrix.