Applications of Compound Poisson Approximation .-I. U . Rurhotrr, 0. C:hr!j.scsaplaino~u, a ~ ~ d E:. Vu,qgclato~u : E. Vaggelatou 5 EOMOk7) + ElMl(L7) > 0 and for all bounded g N R. where ML(g) := + 1) &v(P,Q ) :=

doi:10.1201/9781420036084-18

Chapter

Applications of Compound Poisson Approximation .-I. U . Rurhotrr, 0. C:hr!j.scsaplaino~u, a ~ ~ d E:. Vu,qgclato~u

ABSTRACT

ABSTRACT Stein's met hod for compound Poisson approximation has not been as widely applied as in the Poisson context. One reason for this is that the bounds on the solutions of the Stein Equation are in general by no means as good as for Poisson approximation. Here. we illustrate how new bounds on the solutions have radically changed the situation, provided that the parameters of the approximating compound Poisson distribution satisfy certain conditions. The results obtained in this way are every bit as satisfactory as those obtained in the Poissoii context.