Non-Parametric Estimation of a Renewal Function Based on Histogram

Use of Direct Rieman-Stieltzes Integration Method

Abstract

When the statistical data such as failure data, which are realizations of an i.i.d. random variable, are given, the histogram is often used to understand the underlying distribution property. In this paper, we propose a non-parametric algorithm to estimate the renewal function from the histogram. The estimation algorithm is based on the direct Rieman-Stieltzes integration method. Also, it can be improved in terms of estimation accuracy by applying the interpolation with the spline function or the radial basis function neural network. Finally, in numerical examples, we evaluate the proposed algorithm and its improved versions, and refer to the potential applicability of them.