Estimation of parameters of regularly varying distributions with an application on planetary perturbations on comets

An important class of heavy-tailed distributions is the regularly varying distributions of which the stable distributions are a sub-class. As the stable distributions, the regularly varying distributions can be described by four parameters that determine the tail heaviness, asymmetry, scale and position respectively. In this talk we present at first a method for estimating these parameters by using the order statistics. Then the method is applied to a set of planetary perturbations of a huge number of comets during close encounters with planets in order to give a statistical description of these perturbations.