Sulla stima del parametro di forma di distribuzioni a variazione regolare

Abstract

When the problem of estimating the parameters of a probability distribution is not easy because of too many parameters or the complexity of the analytical form of the distribution, the preliminary estimation of some parameters can usefully simplify the general estimation problem. We consider some very general probability densities which are regularly varying at + oo or at the endpoint of their support, with index a, and having a shape parameter k. In the paper we obtain some relations between k and a. Since a takes the meaning of parameter of regular variation of the upper tail of the distributions and it can be estimated in the context of the tail estimation of a distribution, then the shape parameter k can also be estimated directly by means the above said relations.