This paper addresses a parameter estimation problem for Markov-modulated compound
Poisson process (MMCPP) and compound Markovian arrival process (CMAP). MM-CPP and
CMAP are extended from Markov-modulated Poisson process (MMPP) and Markovian arrival
process (MAP) by combining compound Poisson process (CPP). The EM (expectation-maximization)
algorithm is well known as an effective method in order to perform the statistical
estimation for the family of MAPs. In this paper, we develop the EM algorithm for
MMCPP and CMAP by using the similar technique to the forward-backward algorithm of
hidden Markov model (HMM). In particular, we derive concrete estimation algorithms
for MMCPP and CMAP whose outputs are given by exponential distributions or multivariate
normal distributions. Copyright 2007 ICST.
