Asymptotic laws for upper and strong record values in the extreme domain of attraction and beyond

Asymptotic laws of records values have usually been investigated as limits in type. In this paper, we use functional representations of the tail of cumulative distribution functions in the extreme value domain of attraction to directly establish asymptotic laws of records value, not necessarily as limits in type and their rates of convergences. Results beyond the extreme value value domain are provided. Explicit asymptotic laws concerning very usual laws and related rates of convergence are listed as well. Some of these laws are expected to be used in fitting distribution.