Some Skew-Symmetric Distributions Which Include the Bimodal Ones

Abstract

The class of skew-symmetric distributions has received much attention in recent years. In this article, we introduce two distributions which can capture the skew-symmetric unimodal (e.g., skew-Laplace, skew-normal) and the skew-symmetric bimodal ones systematically. Their natural generalizations of the skew-Laplace and the skew-normal distributions provide greater flexibility in modeling real data distributions. These models also avoid the identifiability problems of using mixtures to fit bimodal data. The stochastic representations that provide the random number generation algorithms are presented. The explicit forms of the central moments indicated that the proposed distributions have wide ranges of the skewness and kurtosis measures.

Keywords:

• Skew-symmetric
• Gaussian
• Skew-normal
• M-Wright
• Mittag-Leffler
• Skew-Laplace
• Airy

Mathematics Subject Classification:

• Primary 47N30
• Secondary 97K70
• 97K80