Nonparametric Estimation of Integral Functionals for Semi-Markov Processes with Application in Reliability
Nikolaos Limnios, Brahim Ouhbi · Birkhäuser Boston eBooks · 2008
This chapter is concerned with moment calculus and estimation of integral functionals of semi-Markov processes. We prove that the n th moment performance function verifies the Markov renewal equation and we derive a simple formula for the first two moments of the integral functional in the finite-state semi-Markov case. We propose an estimator for each one of the two quantities. then we prove their asymptotic properties. We end this chapter by proposing the confidence intervals for the first moment. As an illustration example, we give a numerical application.