ABSTRACT
This chapter outlines some special processes useful in applications and have illustrated the derivation of their simpler properties. It explains why many physical processes can be approximated closely by a Poisson process, since they can be described in terms of a superposition. The chapter focuses on point processes which have simple specifications in terms of the sequence of intervals. It provides a point process may be specified either in terms of counts of points in sets or in terms of its interval sequence. The Poisson process also provides a natural starting point for the construction of processes with more complex structure and indeed many important special processes are generalizations of it. Most of the special point processes studied have been introduced directly via some plausible generating mechanism defined from first principles. As a model of clusters of cars along a one-lane road neither model is really satisfactory, because in that application the natural clusters are not overlapping.
