Method of Moments for the Estimation of the Probability Density Parameters in Correlated Semi-synchronous Event Flow of the Second Order

We consider a correlated semi-synchronous event flow of the second order with two states; it is one of the mathematical models for an incoming stream of claims (events) in modern digital integral servicing networks, telecommunication systems and satellite communication networks. We obtain an explicit form for a probability density of the values of the interval duration between the moments of the events occurrence and an explicit form of the joint probability density of the values of the adjacent intervals durations. We solve the problem of estimating the probability density parameters by the method of moments for general and special cases of setting the flow parameters. The results of statistical experiments performed on a flow simulation model are given.