Logarithmic Transformations for Extrapolative Estimation of Probability Tails

The attractiveness of extrapolative methods exploiting extreme value theory for the estimation of probability tails is limited by the fact that they are not applicable to distributions outside the exponential family. We provide a way to extend their applicability to virtually all distributions of practical interest by introducing suitable logarithmic transformations and proving that they induce the desired extreme value properties in the transformed distributions. We also present examples of the proposed procedure, applied to initial distributions from the diverse classes.