Stability postulate
In probability theory, to obtain a nondegenerate limiting distribution of the extreme value distribution, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size. If formula_1 are independent random variables with common probability density function then the cumulative distribution function of formula_3 is If there is a limiting distribution of interest, the stability postulate states the limiting distribution is some sequence of transformed "reduced" values, such as formula_5, where formula_6 may depend on "n" but not on "x". To distinguish the limiting cumulative distribution function from  the "reduced" greatest value from "F"("x"), we will denote it by "G"("x"). It follows that "G"("x") must satisfy the functional equation This equation was obtained by Maurice René Fréchet and also by Ronald Fisher. Boris Vladimirovich Gnedenko has shown there are "no other" distributions satisfying the stability postulate other than the following: