On the multivariate Laplace distribution

Abstract

In this letter, we discuss the multivariate Laplace probability model in the context of a normal variance mixture model. We briefly review the derivation of the probability density function (pdf) and discuss a few important properties. We then present two methods for estimating its parameters from data and include an example of usage, where we apply the model to represent the statistics of the discrete Fourier transform coefficients of a speech signal. Since the pdf is given in closed form, and the model parameters can be easily obtained, this distribution may be useful for representing multivariate, sparsely distributed data, with mutually dependent components.