Maximum Likelihood Estimation of Parameters in Renewal and Markov‐renewal Processes

Summary Sampling procedures using randomized observation‐points are suggested for estimating parameters in renewal and Markov renewal models. The usual asymptotic properties of the maximum likelihood method are shown to hold. The method we suggest provides a solution to the ML estimation problem in either or both of the following situations: (i) observations on between‐event intervals are unavailable, (ii) the interval densities are unknown or difficult to evaluate while their Laplace‐Stieltjes transforms are known.