Gatha Cognition®
Perception, Learning and Reasoning

#### Bivariate Extremes: Probabilistic Results

Statistical Theory of Extremes

229-268

Bivariate asymptotic distributions , Univariate extremes , Correlation , Regression , Bivariate reduced extremes

An asymptotic distribution of bivariate extremes is studied to obtain the asymptotic probabilistic behaviour and to provide bivariate models of (asymptotic) extremes. The distribution of bivariate extremes and the limiting distribution of maxima are discussed with complementary basic, correlation and regression results. The classical correlation coefficient is linearly invariant. Orthogonal polynomials with respect to $\mathrm{ \Lambda(X) }$  is used to improve the regression lines.