合肥工业大学学报（自然科学版）
閤肥工業大學學報（自然科學版）
합비공업대학학보（자연과학판）
JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY(NATURAL SCIENCE)
2010年
3期
464-466,477
,共4页
上负相关%一致变化尾%控制变化尾%长尾%精确大偏差
上負相關%一緻變化尾%控製變化尾%長尾%精確大偏差
상부상관%일치변화미%공제변화미%장미%정학대편차
upper negatively dependent(UND)%consistently varying tail%dominately varying tail%long tail%precise large deviation(PLD)
随机变量和尾概率性状的研究是保险精算领域的热门问题,而随机变量和的精确大偏差则精确刻画了其尾概率的极限性态.文章分别研究了一列同分布(但不一定独立)随机变量确定和以及随机和的精确大偏差,得到如下结果:如果这列随机变量带一致变化尾,是上负相关的,并且在左直线无支撑,则它们确定和以及随机和的精确大偏差结果均成立.
隨機變量和尾概率性狀的研究是保險精算領域的熱門問題,而隨機變量和的精確大偏差則精確刻畫瞭其尾概率的極限性態.文章分彆研究瞭一列同分佈(但不一定獨立)隨機變量確定和以及隨機和的精確大偏差,得到如下結果:如果這列隨機變量帶一緻變化尾,是上負相關的,併且在左直線無支撐,則它們確定和以及隨機和的精確大偏差結果均成立.
수궤변량화미개솔성상적연구시보험정산영역적열문문제,이수궤변량화적정학대편차칙정학각화료기미개솔적겁한성태.문장분별연구료일렬동분포(단불일정독립)수궤변량학정화이급수궤화적정학대편차,득도여하결과:여과저렬수궤변량대일치변화미,시상부상관적,병차재좌직선무지탱,칙타문학정화이급수궤화적정학대편차결과균성립.
The study on asymptotic behavior of tail probability for the sums of random variables is much popular in actuarial fields, and precise large deviations can exactly characterize it. In this present paper, precise large deviations for determinated sums and random sums of a sequence of identical distributed (not necessarily independent) random variables are considered. The obtained results are as follows: if the random variables with consistently varying tails are upper negatively dependent and have no supportment in the left line, then precise large deviations for determinated sums and random sums all hold.
