A note on the infinite divisibility of a class of transformations of normal variables

TL;DR

This paper investigates when certain transformations of normal variables result in infinitely divisible distributions, providing characterizations and relating findings to known skewing mechanisms.

Contribution

It characterizes a class of density-based transformations of normal variables that lead to non-infinitely divisible distributions, connecting with existing skewing methods.

Findings

Identifies conditions under which transformed normal variables are not infinitely divisible.

Relates the transformations to known skewing mechanisms.

Provides theoretical characterization of the transformations.

Abstract

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We relate our result with some known skewing mechanisms.