The level sets obtained from an equal weights isotonic regression are often of interest. Here we derive the joint distribution of the sizes of the level sets ordered from largest to smallest and show they have the same distribution as three other processes. We also establish some recurrence...

In this paper, we introduce a new copula-based dependence order to compare the relative degree of dependence between two pairs of random variables. Relationship of the new order to the existing dependence orders is investigated. In particular, the new ordering is stronger than the partial...