  We introduce a new functional representation of probability density functions
(PDFs) of non-negative random variables via a product of a monomial factor and
linear combinations of decaying exponentials with complex exponents. This
approximate representation of PDFs is obtained for any finite, user-selected
accuracy. Using a fast algorithm involving Hankel matrices, we develop a
general numerical method for computing the PDF of the sums, products, or
quotients of any number of non-negative random variables yielding the result in
the same type of functional representation. We present several examples to
demonstrate the accuracy of the approach.
