From extended regular variation to regular variation with application in extreme value statistics

This paper aims to provide a study of a variety of concepts involving power behavior of eventually positive functions which, falling under the umbrella of the Theory of Regular Variation and its second order refinements, are prone to application in Extreme Value Theory. To this extent, some well-known properties shall be resumed, others will be designed with the ultimate purpose of establishing a relation between regular variation and extended regular variation of second order. As a by-product, new ways of looking at some common estimators for the extreme value index, in particular the maximum likelihood estimator, will be unveiled.