In the multivariate case, the empirical dependence function, defined as the empirical distribution function with reduced uniform margins on the unit interval, can be shown for an i.i.d. sequence to converge weakly in an asymptotic way to a limiting Gaussian process. The main result of this paper...

We establish the functional central limit theorem and law of the iterated logarithm for the Pickands estimator of the dependence function of a bivariate extreme-value distribution. Our methods are based on general results for sums of random variables taking values in Banach spaces.

Let Fn and Gn denote the Kaplan-Meier product-limit estimators of lifetime distributions based on two independent samples, and let Fninv and Gninv denote their quantile functions. We consider the corresponding P-P plot Fn(Gninv) and Q-Q plot Fninv(Gn), and establish strong approximations of...

A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that...

This paper concerns an asymptotic expansion for the distribution of the sum of independent zero-one random variables in case where this surn has variance [sigma]n2 -- [infinity]. The expansion presented is given to the order O([sigma]n-2). An application to the study of the exact rate of...

Let Sn = X1 + ... + Xn denote the nth partial sum of an i.i.d. sequence of random variables having positive mean [mu] and finite variance [sigma]2, and let N(s) = minlcubn [greater-or-equal, slanted] 0: Sn+1 srcub denote the corresponding renewal process. We investigate the strong limiting...

We establish the consistency of a non-parametric estimator of bivariate extreme-value distributions.