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MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS IN RENEWAL AND MARKOV‐RENEWAL PROCESSES
Author(s) -
Basawa I. V.
Publication year - 1974
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1974.tb00911.x
Subject(s) - mathematics , renewal theory , markov chain , markov renewal process , maximum likelihood , statistics , laplace transform , event (particle physics) , estimation , interval estimation , laplace's method , interval (graph theory) , markov process , markov model , confidence interval , mathematical optimization , computer science , markov property , bayesian probability , combinatorics , mathematical analysis , engineering , physics , systems engineering , quantum mechanics
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.