not a logistic distribution). Note that . Proofs 4. Let , then the cumulative distribution of is: which is the cdf for . 5. Let , then the cumulative distribution of is: which is the cumulative distribution of . See also Extreme Value Theory (Univariate Theory) Fisher–Tippett–Gnedenko theorem Generalized Pareto distribution German tank problem, opposite question of population maximum given sample maximum Pickands–Balkema–De Haan theorem References Further reading Continuous distributions Extreme value data Location-scale family probability distributions Stability (probability)