Walsh Series Expansions of Probability Distributions

This paper discusses the representation of probability distribution functions by Walsh series expansions. Generally, such expansions may be employed for the representation of multivariate distributions. However, we confine attention here to univariate and bivariate distributions. The resulting expansions are consequently utilized in the derivation of useful expressions for the moments of corresponding probability distributions. Applications of Walsh expansions of probability distributions are further illustrated by computing output moments for some general classes of nonlinear systems.