Numerical inversion of Laplace transforms of probability distributions

We present a simple algorithm for numerically inverting Laplace transforms. The algorithm is designed especially for probability cumulative distribution functions, but it applies to other functions as well. Since it does not seem possible to provide effective methods with simple general error bounds, we simultaneously use two different methods to confirm the accuracy. Both methods are variants of the Fourier-series method. The first, building on Dubner and Abate and Simon, Stroot, and Weiss, uses the Bromwich integral, the Poisson summation formula and Euler summation; the second, building on Jagerman, uses the Post–Widder formula, the Poisson summation formula, and the Stehfest enhancement. The resulting program is short and the computational experience is encouraging.