MAP fitting by count and inter-arrival moment matching

Abstract

We identify key characteristics of a correlated point process which include moments of the time between arrivals as well as measures of variability and correlation obtained from the counting process over different time intervals. A computational framework to calculate these characteristics is presented for the general MAP(n). We present simple closed-form-expressions for the key characteristics and an efficient algorithm to fit a MAP(2) to a point process. The contributions of this article include 1) developing a computational framework, in the form of partial-moment differential equations (PMDEs) and linear equations to derive a compact matrix exponential expression for the count process moments of a MAP(n), 2) developing an efficient and accurate algorithm to fit a MAP(2) based on count and inter-arrival moments. © 2018, © 2018 Taylor & Francis.