Normal Approximation and Edgeworth Series for F(x)

Abstract

It will be apparent from the foregoing chapters that the generalized Poisson function F(x) which gives the distribution of the annual result of an insurance operation is, unfortunately, complicated as regards computation particularly in practical applications. Direct methods of attack on the numerical treatment of F(x) often lead to very cumbersome expressions so that it is, in general, not easy to deal with problems concerned with, for example, different methods of reinsurance, net retentions, and safety loadings. Furthermore, it is extremely difficult to obtain a broad survey of the problems. Even if the nature of the problems justifies the more detailed computations, simple working approximations are necessary and it follows that one of the problems of applied risk theory is the finding of proper approximations.