A symmetric transformation of Tukey's g-h family of distributions

Accepted - December 2024

Abstract

This class of distributions is a special case of Tukey's g-h family of distributions whose shape is symmetric, which allow approximating several different symmetric distributions. Many research consider that the class of Tukey's h distributions depend only the parameter h which controls the tails heaviness, we include the parameter g to obtain the symmetric transformation of Tukey's g-h distribution which allow approximating the even moments (e.g. kurtosis). In this paper, we calculate a closed form expression for the probability density function of the symmetric transformation Tukey's g-h family of distributions, which allows us to easily compute probabilities, central moments and related measures.