On asymptotic distributions of exceedance statistics

In this study, two independent samples X1,X2,…,XnX1,X2,…,Xn and Y1,Y2,…,YmY1,Y2,…,Ym with respective distribution functions FF and QQ are considered. The joint asymptotic distributions of exceedance statistics defined as the number of YY observations falling into a random interval of order statistics constructed from the XX sample is investigated. The results can be used in the context of a two-sample problem.

► Different random thresholds are considered.
► Their exact distribution functions are obtained.
► Asymptotic properties are investigated.
► Tables are given for different levels.