APPROXIMATIONS FOR THE RENEWAL FUNCTION

This paper describes an accurate, computable approximation for evaluat ing the renewal function (RF). The method uses Pade approximants to co mpute the RF near the origin and switches to the asymptotic values far ther from the origin. There is a polynomial switchover function in ter ms of the coefficient of variation of the distribution, enabling one t o determine a priori if the asymptotic value can be used instead of co mputing the Pade approximant. The results are tested with the truncate d Gaussian distribution. The method yields a set of approximants to th e RF that cue re-usable, and can be used to compute the derivative and the integral of the RF. Results for the RF are within 1% of the optim al solution for most coefficients of variation.