A multivariate extension to the Exponentially-modified Gaussian distribution

Sandhya Prabhakaran

Keywords: skewness, exponentially-modified Gaussian, multivariate data analysis, single cell RNA seq data

TL;DR: We propose a multivariate extension to the univariate Exponentially-modified Gaussian so that the first three moments of the multivariate data can be described all at once.

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.

Category: Stuck paper: I hope to get ideas in this workshop that help me unstuck and improve this paper