The Asymptotic Distribution of Maxima in Bivariate Samples
Janet W. Campbell, Chris P. Tsokos · Journal of the American Statistical Association · 1973
This article investigates the joint distribution, as n→ ∞, of the maxima in a sample of n independent observations of a bivariate random variable (X,Y). A method is presented for deriving the asymptotic distribution of the maxima provided that (1) X and Y possess asymptotic extreme-value distributions and (2) the probability element dF(x,y) has a canonical series expansion. Applied to the bivariate normal distribution, this method confirms the known fact that correlated normal maxima are asymptotically uncorrelated. Applied to the bivariate gamma and compound correlated bivariate Poisson distributions, the method establishes that maxima from these distributions are also asymptotically uncorrelated.