Abstract
This paper proposes a new estimation method of the renewal function from i. i. d. observations of the inter-arrival time, using a radial basis function (RBF) type of neural network. The basic idea is to solve numerically the discritized renewal equation based on the corresponding empirical distribution function to the observations. The RBF neural network is applied to approximate the underlying empirical distribution. Throughout numerical experiments, we show that the proposed method can estimate the renewal function with higher precision than existing statistical methods for a pattern data.
