Let be i.i.d. non-negative random variables with d.f. F and Laplace transform L. Let N be integer valued and independent of . In many applications one knows that for and a function where in turn is the solution of an equation . On the basis of a sample of size n the authors derive an estimator for by solving where is the emprirical version of L. This estimator is then used to derive the asymptotic behaviour of . The authors include five examples, some of which are taken from isurance mathematics
