Stein’s method for conditional compound Poisson approximation

The occurrence of rare events can often be well described by a compound Poisson distribution. However, one can only start modelling the occurrence of rare events after such events have happened, thus a conditional compound Poisson distribution is more appropriate in applications. In this note, we develop Stein’s method for conditional compound Poisson approximation. Several applications are given to demonstrate the advantage of the direct approach of Stein’s method.