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 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 parameters measuring the location θ, the scale σ,...