An abundance of high quality data sets requiring heavy tailed models necessitates reliablemethods of estimating the shape parameter governing the degree of tail heaviness.The Hill estimator is a popular method for doing this but its practical use isencumbered by several difficulties. We show...

In R2 the integral of a regularly varying (RV) function f is regularly varying only if f is monotone. Generalization to R2 of the one-dimensional result on regular variation of the derivative of an RV-function however is straightforward. Applications are given to limit theory for partial sums of...

Out of n i.i.d. random vectors in d let X*n be the one closest to the origin. We show that X*n has a nondegenerate limit distribution if and only if the common probability distribution satisfies a condition of multidimensional regular variation. The result is then applied to a problem of density...

Let X1, X2,..., Xn be n independent, identically distributed, non negative random variables and put and Mn = [logical and operator]ni=1 Xi. Let [varrho](X, Y) denote the uniform distanc distributions of random variables X and Y; i.e. . We consider [varrho](Sn, Mn) when P(X1x) is slowly varying...