On Standard Log-Fréchet and Log-log-Fréchet Laws

As the well known extreme value law, the Fréchet law, is the standard example of ‘‘heavy tail,’’ the log-Fréchet and the log-log-Fréchet laws are standard examples of ‘‘super heavy tails.’’ New characterizations of max-domains of attraction of standard log-Fréchet and log-log-Fréchet laws, based on integral representations, are obtained in this article. Several illustrations are discussed including an example involving the Tracy-Widom distribution.