Thesis, Undergraduate (BS in applied mathematics)

The renewal function is one of the stochastic processes that observe a behaviour of a given distribution. It is a sum of the distribution that were obtained from events that occured at a given span of time. A problem arising from using the renewal function is that it is unbounded which makes it difficult to evaluate numerically. Thus , approximation was done. The study approximated the renewal function by truccating the upper bound to a finite one then measure its performance through the corresponding percentage error associated with the approximation. Gamma distribution was usee in thisstudy because it follows a Poison process at a positive integer a. The approximated renewal function of the Gamma distribution was evaluated numerically using Maple V. The numerical results for the percentage error as well as the graphical illustartions was obtained using Microsoft Excel 2007. The numerical results of the study arrived at the conclusion that the approximation is at its best performance when the values of T are very small, relatively smaller when N issmaller at an increasing A.