Poisson approximations of multinomial distributions and point processes

Surveillance of Poisson and Multinomial Processes

As time passes, change occurs. With this change comes the need for surveillance. One may be a technician on an assembly line and in need of a surveillance technique to monitor the number of defective components produced. On the other hand, one may be an administrator of a hospital in need of surveillance measures to monitor the number of patient falls in the hospital or to monitor surgical outc...

Poisson processes (and mixture distributions)

Transforming spatial point processes into Poisson processes

In 1986, Merzbach and Nualart demonstrated a method of transforming a two-parameter point process into a planar Poisson process of unit rate, using random stopping sets. Merzbach and Nualart's theorem applies only to a special class of point processes, since it requires two restrictive conditions: the (F4) condition of conditional independence and the convexity of the 1-compensator. The (F4) co...

Thinning spatial point processes into Poisson processes

This paper describes methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where one simulates backwards and forwards in order to obtain the thinned process. In the case...

Efficient simulation of non-Poisson non-stationary point processes to study queueing approximations

A nonstationary point process can be efficiently simulated by exploiting a representation as the composition of a rate-one process and the cumulative arrival rate function, provided that an efficient algorithm is available for generating the rate-one process, as is the case for stationary renewal processes, Markov modulated Poisson processes and many other processes. Overall efficiency can be a...