负相协重尾随机变量和的尾概率的渐近性的若干注记

Notes on the Asymptotics of the Tail Probabilities of Sums for Negatively Associated Random Variables with Heavy Tails

摘要: 本文得到了同分布负相协重尾随机变量和的最大值、随机个和的最大值尾概率的渐进性质\bd 所得到的结果削弱了Wang和Tang (Statist. Prob. Lett., 68, 287--295, 2004)^1的Theorem 2.1的矩条件, 在与1的Theorem 2.2不同的条件下得到了相应的结果, 并且都解除了上述1的结果中对随机变量的支撑的限制.

Abstract: This paper obtains some asymptotics for the tail probabilities of maximum of sums, random sums and maximum of idetically distributed, negatively associated random variables with heavy tails. The obtained results weaken the conditions of the moments of Theorem 2.1 in Wang and Tang (Statist. Prob. Lett., 68, 287--295, 2004). We also discuss the conditions of Theorem 2.2 of 1 and remove the restrictions of the supports of random variables.