On the asymptotics of numbers of observations in random regions determined by order statistics
A. Dembińska and G. Iliopoulos
In this paper we consider random variables counting numbers of observations that fall into regions determined by extreme order statistics and Borel sets. We study multivariate asymptotic behavior of these random variables and express their joint limiting law in terms of independent multinomial and negative multinomial laws. First we give our results for samples with deterministic size, next we explain how to generalize them to the case of randomly indexed samples.
Key words and phrases: Order statistics; Weak limit theorems; Asymptotic independence;
Randomly indexed samples.