Estimation of marginal excess moments for Weibull-type distributions

We consider the estimation of the marginal excess moment(MEM), which is defined for a random vector(X,Y)and a parameter beta > 0 as E[(X-QX(1-p))(beta)(+)|Y > Q(Y )(1 - p) ] provided E|X|(beta )< infinity, and where y(+ ): = max (0, y), Q(X )and Q(Y )are the quantile functions of X and Y respectively, and p is an element of (0, 1). Our interest is in the situation where the random variable X is of Weibull-type while the distribution of Y is kept general, the extreme dependence structure of(X,Y)converges to that of abivariate extreme value distribution, and we let p down arrow 0 as the sample sizen -> infinity. By using extreme value arguments we introduce an estimator for the marginal excess moment and we derive its limiting distribution. The finite sample properties of the proposed estimator are evaluated with a simulation study and the practical applicability is illustrated on a dataset of wave heights and wind speeds