“Asymptotic Independence of Bivariate Extremes”, 1964-11-01 (; backlinks; similar):
1960 has given a necessary and sufficient condition for asymptotic independence of two extremes for a sample from bivariate population. We shall obtain such a condition for asymptotic independence of all the 4 extremes X, X’, Y and Y’. It assumes a very simple form when f(x, y) is symmetrical in x and y, and the marginal p. d. f. of x and y have the same form.
Under these conditions on the p. d. f., a modification is possible in the condition given by 1960 which reduces to one given by 1954 for other purpose. It is further shown that extremes for samples from bivariate normal population satisfy our condition if |p| < 1, where p is the population correlation coefficient. 1958 and 1960 have proved a particular result for asymptotic independence of only two extremes X and Y in the normal case.