Expression for the skew normal distribution specifying up to third-order moments independently

—Analysis of skewness of brand value—

Abstract

The purpose of this study is to propose the expression for the skew normal distribution by specifying up to third-order moments independently.We developed the new density function which can specify mean, variance, and skewness directly by translating the parameters of skew normal distribution.This method enabled us to estimate skewness of latent variable directly and to compare distribution between groups.A simulation study indicated validity of parameter estimation, and the analysis of brand value data showed effectiveness of this method.Parameter estimation was performed via Hamiltonian Monte Carlo Method.