The epsilon-skew-normal distribution for analyzing near-normal data

A family of asymmetric distributions, which first appeared in Fechner (1897, Kollectivmasslehre. Leipzig, Engleman) is reparameterized using a skewness parameter epsilon and named the epsilon-skew-normal family. It is denoted by ESN(theta, sigma, epsilon). Its basic properties such as the relationship between the mean and mode, and its higher-order moments are examined. They are used to obtain simple estimators of the parameters measuring the location theta, the scare sigma, and the skewness epsilon. The maximum likelihood estimates are derived and it is shown that the estimators of theta and sigma are asymptotically independent. The estimators reduce properly to the normal case when epsilon = 0. The ESN(theta, sigma, epsilon) can be used both as a model and as a prior distribution in Bayesian analysis. The posterior distributions in both cases are unimodal, and the modes are available in closed form. (C) 2000 Published by Elsevier Science B.V. All rights reserved.