Why Skew Normal: A Simple Pedagogical Explanation

José Guadalupe Flores Muñiz ； Vyacheslav V. Kalashnikov ； Nataliya Kalashnykova ； Olga Kosheleva ； Vladik Kreinovich

《International Journal of Intelligent Technologies and Applied Statistics》 11卷2期 (2018/06) Pp. 113-120

https://doi.org/10.6148/IJITAS.201806_11(2).0004

摘要

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 does not 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.

關鍵字

Skew normal distribution ； Maximum entropy ； Normal distribution ； Skewness ； Third moment