Shape mixtures of skew-t-normal distributions: characterizations and estimation

摘要

This paper introduces the shape mixtures of the skew-t-normal distribution which is a flexible extension of the skew-t-normal distribution as it contains one additional shape parameter to regulate skewness and kurtosis. We study some of its main characterizations, showing in particular that it is generated through a mixture on the shape parameter of the skew-t-normal distribution when the mixing distribution is normal. We develop an Expectation Conditional Maximization Either algorithm for carrying out maximum likelihood estimation. The asymptotic standard errors of estimators are obtained via the information-based approximation. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.