Partitioning and Thinning of a Renewal Process. Let N(t) be a renewal process with inter-renewal distribution F. Suppose each renewal time is independently assigned to be a type i renewal with...

Partitioning and Thinning of a Renewal Process. Let N(t) be a renewal process with inter-renewal distribution F. Suppose each renewal time is independently assigned to be a type i renewal with probability pi, for i = 1,...,m, where p1 + ··· + pm = 1. Let Ni(t) denote the number of type i renewals up to time t. These processes form a partition of N(t) in