Parameter estimation for the heavy tailed distributions with the empirical distribution

Heavy-tailed distributions have been observed in many natural phenomena including hydrology, geology, electro technology, informatics, physics and insurance. One of the most challenging characteristics of heavy-tailed distribution is their high or even infinite variance or burstiness. Heavy-tailed distributions are the distributions, the tails of which cannot be cut off. So, we cannot neglect the large-scale but rare events. Te most evident and natural problem of statistical estimation connected with heavy tailed distributions are the problem of their parameter estimation. For estimating their parameter, known statistical procedures can be used, for example, estimation methods of Hill, de Haan and others. Therefore the purpose of this article is the new method of estimation of parameter for heavy tailed distributions using the empirical distributions.

کلیدواژه ها:

Empirical distribution ، Glivenko theorem ، Least squats method