32 CL ´ EMENT DOMBRY, MICHAEL FALK, MAXIMILIAN ZOTT Computation of the distribution of X$_{N}$$_{(}$$_{k}$$_{)}$ for an arbitrary k ≥ 2 is much more complex, but manageable. Computation of the limit distribution of X$_{N}$$_{(}$$_{k}$$_{)}$ , properly linearly standardized, as k tends to infinity, is an open problem. For the univariate case we refer to Galambos (1987, Section 6.4). References Arnold, B. C. , Balakrishnan, N. , and Nagaraja, H. N. (1998). Records . Wiley Series in Probability and Statistics. Wiley, New York. Aulbach, S. , and Falk, M. (2012 a ). Local asymptotic normality in δ - neighborhoods of standard generalized Pareto processes. J. Statist. Plann. In- ference 142 , 1339–1347. doi:10.1016/j.jspi.2011.12.011 . Aulbach, S. , and Falk, M. (2012 b ). Testing for a generalized Pareto process. Electron. J. Stat. 6 , 1779–1802. doi:10.1214/12-EJS728 . Aulbach, S. , Falk, M. , and Hofmann, M. (2013). On max- stable processes and the functional D -norm. Extremes 16 , 255–283. doi:10.1007/s10687-012-0160-3 . Aulbach, S. , Falk, M. , Hofmann, M. , and Zott, M. (2014). Max- stable processes and the functional D -norm revisited. Extremes 18 , 191–212. doi:10.1007/s10687-014-0210-0 . Balkema, A. A. , and Resnick, S. I. (1977). Max-infinite divisibility. J. Appl. Probab. 14 , 309–319. doi:10.2307/3213001 . Billingsley, P. (1968). Convergence of Probability Measures . Wiley Series in Probability and Mathematical Statistics, 1st ed. Wiley. Buishand, T. A. , de Haan, L. , and Zhou, C. (2008). On spatial ex- tremes: with application to a rainfall problem. Ann. Appl. Stat. 2 , 624–642. doi:10.1214/08-AOAS159 . Coles, S. G. , Heffernan, J. E. , and Tawn, J. A. (1999). Dependence measure for extreme value analyses. Extremes 2 , 339–365.