Fitting combinations of exponentials to probability distributions

Two techniques are described for approximating distributions on the positive half-line by combinations of exponentials. One is based on Jacobi polynomial expansions, and the other on the logbeta distribution. The techniques are applied to some well-known distributions (degenerate, uniform, Pareto, lognormal and others). In theory, the techniques yield sequences of combination of exponentials that always converge to the true distribution, but their numerical performance depends on the particular distribution being approximated. An error bound is given in the case the logbeta approximations. Copyright © 2006 John Wiley & Sons, Ltd.