Discrete Approximation of a Mixture Distribution via Restricted Divergence

Mixture distributions arise inmany application areas, for example, as marginal distributions or convolutions of distributions. We present amethod of constructing an easily tractable discretemixture distribution as an approximation to a mixture distribution with a large to infinite number, discrete or continuous, of components. The proposed DIRECT (divergence restricting conditional tesselation) algorithm is set up such that a prespecified precision, defined in terms of Kullback-Leibler divergence between true distribution and approximation, is guaranteed. Application of the algorithm is demonstrated in two examples. Supplementary materials for this article are available online.