Gatha Cognition®
Perception, Learning and Reasoning

#### Analitic Statistical Choice for Univariate Extremes

Statistical Theory of Extremes

157-172

Variational approach , Locally optimal approach , Fréchet distribution , Gumbel distribution , Weibull distribution

Method of statistical choice between Weibull, Gumbel and Fréchet distribution is described. Locally optimal approach and variational approach are discussed to illuminate the problem from two points of view. Analysis begins with samples of reduced values and extended for generalization. The variational approach is coincident with the locally optimal approach. However, there does not exist an optimal procedure for statistical choice based on $Q_n$ .