Further developments on sufficient conditions for negative dependence of random variables

Negative dependence in the balls and bins experiment with applications to order statistics

“…This study was initiated by Tukey [20] and Barlow and Proschan [2], developed by Karlin and Rinott [11], Block et al [3], Shanthikumar [19], Kim and David [14], and Boland et al [5], and has been continued until the more recent papers by Khaledi and Kochar [13], Hu and Zhu [9], Hu and Yang [8], Schmitz [17], and Avérous et al [1].…”

“…In Definition 1.1, by conditioning on one random variable instead of a set of random variables, we get the other three notions of negative dependence, denoted by NRD 1 , NLTD 1 and NRTD 1 , which were considered by Hu and Yang [8]. NRD 1 is also termed as NDS in [4].…”

“…NRD 1 is also termed as NDS in [4]. Hu and Yang [8] gave three structural theorems which state the conditions under which the underlying random vectors are NRD 1 , NLTD 1 and NRTD 1 , respectively.…”

“…The relationships among NRD, NLTD and NRTD are still under our investigation. It is worthwhile to mention that there is no relationship between NRD and NA [10,8].…”

A Central Limit Theorem for Non-Overlapping Return Times

“…As in the proof of Theorem 3.4 of [10], it suffices to show that (3.1) holds for symmetric functions f 1 and f 2 with A 1 = {1, . .…”