%0 Journal Article %A Rassoul Abdelaziz %D 2012 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 62, 2012 %T Estimating of the Renewal Function with Heavy-tailed Claims %U https://publications.waset.org/pdf/11435 %V 62 %X We develop a new estimator of the renewal function for heavy-tailed claims amounts. Our approach is based on the peak over threshold method for estimating the tail of the distribution with a generalized Pareto distribution. The asymptotic normality of an appropriately centered and normalized estimator is established, and its performance illustrated in a simulation study. %P 145 - 150