Using the κ-exponential to deform Gumbel and Gompertz probability distributions

Here we propose the use of the κ-exponential to deform Gumbel and the Gompertz distributions. The κ-exponential is a function of κ-statistics, a statistics which has been developed by G. Kaniadakis, Politecnico di Torino, in the framework of special relativity, and used for statistical analyses involving power law tailed distributions. The exponentiated κ-Gumbel function is also considered, to have a further deformation of the probability distribution.