On the symmetric and skew-symmetric K-distributions

This paper introduces the four-parameter symmetric K-distribution (SKD) and the skew-SKD as models for describing the complex dynamics of machine learning, Bayesian analysis and other fields through simplified expressions with high accuracy. Formulas for the probability density function, cumulative distribution function, moments, and cumulants are given. Finally, an order statistics analysis is provided as well as the distributions of the product and ratio of two SKD random variables are derived.