2024/10/29 by Fraiman, Ricardo, Moreno, Leonardo, Ransford, Thomas
#60B11 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2410.22038
We show how a Cramér-Wold theorem for a family of multivariate probability distributions can be used to generate a similar theorem for mixtures (convex combinations) of distributions drawn from the same family. Using this abstract result, we establish a Cramér-Wold theorem for mixtures of multivariate Gaussian distributions. According to this theorem, two such mixtures can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending only on the total number Gaussian distributions involved and on the ambient dimension. A similar result is also obtained for mixtures of multivariate t-distributions.