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Keywords:

  • Markov;
  • renewal;
  • spatial;
  • maximum likelihood estimation;
  • applications

Abstract

This paper presents an extension to the the Ivanoff–Merzbach renewal process. The Ivanoff–Merzbach process is a natural analogue to the one-dimensional renewal process. Restricting our attention to two dimensions, the focus of the current paper will be formation of this extension, which we will refer to as a Markov renewal process, as well as simulation, estimation and applications to data sets in ecology and forestry. Copyright © 2010 John Wiley & Sons, Ltd.