On the Voigt profile and its dual

TL;DR

This paper reveals that the Voigt profile can be represented as a scale mixture of Gaussians with a Levy distribution, introduces a dual distribution, and discusses algorithms for parameter estimation.

Contribution

It demonstrates that the Voigt profile is a scale mixture of Gaussians with a Levy distribution and introduces the concept of a dual Voigt distribution with related properties.

Findings

Voigt profile as a Gaussian-Levy scale mixture

Existence of a dual Voigt distribution as a normal scale mixture

Algorithms for parameter estimation of the Voigt and dual profiles

Abstract

The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing Levy distribution. A consequence of this result is that there exists a dual of the Voigt distribution, which is itself a normal scale mixture. Both the Dual Voigt and its mixing are transformations, via truncation and reflection, of the Normal and Levy random variables. We discuss the dual Voigt characteristics, propose algorithms for parameter estimation and outline further developments.