Nonparametric estimation of a renewal function in the case of censored sample
Abstract
A renewal process is a counting process which counts the number of renewals that occurs as a function of
time, wherein the durations between successive renewals are random variables independent of one
another, with identical F distributions. The mean value function data is frequently needed in applications
of renewal processes. For the renewal function, open expressions depending on distribution function F
can be calculated from each other. However, even though the distribution function F is known, the renewal
function cannot be obtained analytically except for a few distributions. In this study, in the case that F is
totally unknown, life table management and Kaplan-Meier estimator were used depending on random
right-censored sampling for the estimation of F value. Then, for the estimation of the renewal function
value in the random right-censored data, nonparametric estimators were proposed and the problem of how
to calculate these estimators were discussed.
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