On the Voigt distribution: Characterization and parameter estimation

Gavino Puggioni;Massimo Cannas

2023-01-01

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Abstract

The Voigt profile is the convolution of Gaussian and Cauchy random variables. The Voigt is extensively used in atomic and molecular spectroscopy to represent superposition effects. The lack of a moment-generating function and of a closed form for the density has generated some interest in the literature about parameter estimation. We provide a new characterization of the Voigt profile and its associated dual. We also propose an MCMC algorithm to estimate the posterior distribution of both scale and location parameters. A simulation study demonstrates a better performance of our algorithm compared to other approaches.