Journal of Mathematics and Statistics

Estimation and Reliability for a Special Type of Semi-Markov Process

Vlad Stefan Barbu, Alex Karagrigoriou and Andreas Makrides

Journal of Mathematics and Statistics

Abstract

This work deals with multi-state systems modelled by means of semi-Markov processes. The sojourn times are seen to be independent not identically distributed random variables and assumed to belong to one of two different general classes of distributions so that the first class is closed under maxima and the second one is closed under minima. We obtain maximum likelihood estimators of the parameters of interest under several estimation schemes and investigate their asymptotic properties. Plug-in type estimators are furnished for various quantities related to the system under study.

Copyright

© 2019 Vlad Stefan Barbu, Alex Karagrigoriou and Andreas Makrides. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.