A Multivariate Extension to the Exponentially-Modified Gaussian Distribution

Abstract

The exponentially-modified Gaussian (EMG) distribution is a convolution sum of a univariate Gaussian and an exponential distribution. This has been used to model univariate skewed data such as chromatographic peaks' shape, cell population dynamics from single-cell data and reaction times in neuropsychology. Currently, the EMG is only available in its univariate form. In this work, we propose a multivariate extension to the EMG, called $\textit{mvEMG}$, by using an affine transformation involving rotation, translation and shearing to accommodate for the three moments (mean, variance and skew). We derive statistical properties for mvEMG. Although we demonstrate its performance in synthetic data compared with the multivariate skew normal distribution, we are unable to show its practical applicability, mainly due to lack of efficient sampling strategies and a viable real-world dataset.