ABSTRACT

This chapter deals with the joint limiting distribution of numbers of exceedances of several levels. We present multilevel generalizations of the results on the previous chapter.

Let x1 > · · · > xm be a set of levels. Denote x¯ = (x1, . . . , xm) and let

Nn[a, b) = n∑

i=1 1I{a ≥ Xi > b} (a > b).