Why Skew Normal: A Simple Pedagogical Explanation

Authors

José Guadalupe Flores Muñiz, Universidad Autónoma de Nuevo LeónFollow
Vyacheslav Kalashnikov, Tecnológico de Monterrey (ITESM)Follow
Nataliya Kalashnykova, Universidad Autónoma de Nuevo LeónFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

2-2018

Comments

Technical Report: UTEP-CS-18-11

Abstract

In many practical situations, we only know a few first moments of a random variable, and out of all probability distributions which are consistent with this information, we need to select one. When we know the first two moments, we can use the Maximum Entropy approach and get normal distribution. However, when we know the first three moments, the Maximum Entropy approach doe snot work. In such situations, a very efficient selection is a so-called skew normal distribution. However, it is not clear why this particular distribution should be selected. In this paper, we provide an explanation for this selection.