A nonparametric estimator of the renewal function

A new algorithm for calculating a nonparametric estimator of the renewal function is described. The estimator has negligible bias, and is rapid to compute. Computation time depends upon the type of distribution, but for an exponential distribution, computation time is proportional to n³’/², where n is the sample size, and storage proportion to n¹’/². Simulations of random samples from typical distributions encountered in survival analysis [exponential, Weibull, lognormal, and Dhillon (bathtub) distributions] were used to check the performance of the method, and to choose an array size large enough to reduce the bias of the estimator to an acceptable level. Examples of the logarithm’s use are given, and a C program that computes the estimator is appended.