A novel analytical scheme to compute the n-fold convolution of exponential-sum distribution functions

摘要

A general analytical scheme for computing the n-fold convolution of exponential-sum distribution functions has been developed in this paper. The n-fold convolution is first expressed by multiple sums of recursive integrals. These recursive integrals are then reconstructed with a series of delta functions to avoid separations of integrations. Part of the recursive integrals has been solved analytically by either direct integration or with Maple-like symbolic software packages. The general analytical solution of the n-fold convolution of exponential-sum distribution functions is obtained in two steps: first developing a general pattern of Laplace transform of the recursive integrals, and then performing an inverse Laplace transform operation to the general pattern of the developed Laplace transform. The solution presented in this paper provides another option for computing the n-fold convolution of exponential-sum distribution functions.