A family of asymmetric distributions, which first appeared in Fechner (1897, Kollectivmasslehre. Leipzig, Engleman) is reparameterized using a skewness parameter ε and named the epsilon–skew–normal family. It is denoted by ESN(θ,σ,ε). 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

... [Show full abstract] parameters measuring the location θ, the scale σ, and the skewness ε. The maximum likelihood estimates are derived and it is shown that the estimators of θ and σ are asymptotically independent. The estimators reduce properly to the normal case when ε=0. The ESN(θ,σ,ε) 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.