Precise Large Deviations for Sums of Independent Random Variables with Consistently Varying Tails

DAWEI LU; LIXIN SONG; YING XU

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Precise Large Deviations for Sums of Independent Random Variables with Consistently Varying Tails

机译：尾部一致而变化的独立随机变量之和的精确大偏差

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In this article, we investigate the precise large deviations for a sum of independent but not identical distributed random variables. {X_n, n ≥ 1} are independent non-negative random variables with distribution functions [F_n, n≥ 1}. We assume that the average of right tails of distribution functions F_n is equivalent to some distribution function F with consistently varying tails. In applications, we apply our main results to a realistic example (Pareto-type distribution) and obtain a specific result.

机译：在本文中，我们研究了独立但不相同的分布随机变量之和的精确大偏差。 {X_n，n≥1}是具有分布函数[F_n，n≥1}的独立非负随机变量。我们假设分布函数F_n的右尾部平均值等于具有连续变化的尾部的某些分布函数F。在应用程序中，我们将主要结果应用于实际示例（帕累托型分布）并获得特定结果。

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来源
《Communications in Statistics》 |2014年第3期|28-43|共16页
作者
DAWEI LU; LIXIN SONG; YING XU;
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作者单位

School of Mathematical Sciences Dalian University of Technology Dalian 116023 China;

School of Mathematical Sciences Dalian University of Technology Dalian China;

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原文格式 PDF
正文语种 eng
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关键词
Consistently varying tails; Precise large deviations; Random sums;

机译：不断变化的尾巴;精确的大偏差;随机和;

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专利

1. Precise large deviations for randomly weighted sums of negatively dependent random variables with consistently varying tails [J] . Shen XM, Lin ZY Statistics & Probability Letters . 2008,第18期

机译：尾部一致的负相关随机变量的随机加权和的精确大偏差
2. Precise large deviations for sums of random variables with consistently varying tails in multi-risk models [J] . Wang S, Wang WS Journal of Applied Probability . 2007,第4期

机译：多风险模型中尾部持续变化的随机变量总和的精确大偏差
3. Precise large deviations for sums of random variables with consistently varying tails [J] . Ng KW, Tang QH, Yan JA, Journal of Applied Probability . 2004,第1期

机译：尾部持续变化的随机变量之和的精确大偏差
4. Randomly Weighted Sums of Negatively Associated Random Variables with Heavy Tails [C] . Peng, JiangYan International Conference on Computational Intelligence and Software Engineering;CiSE 2009 . 2009

机译：具有负尾的负相关随机变量的随机加权和
5. Small deviations of sums of random variables. [D] . Garnett, Brian. 2016

机译：随机变量总和的小偏差。
6. Precise large deviations for widely orthant dependent random variables with different distributions [O] . Miaomiao Gao, Kaiyong Wang, Lamei Chen -1

机译：具有广泛分布的正态分布随机变量的精确大偏差
7. Precise Large Deviations for Sums of Random Variables with Consistently Varying Tails [O] . Kai W. Nga, Qihe Tangb, Jia-an Yanc A, 2012

机译：尾部一致变化的随机变量之和的精确大偏差
8. Importance Sampling for Sums of Random Variables With Regularly Varying Tails [R] . Dupuis, P. , Leder, K. , Wang, H. 2006

机译：具有规则变化尾部的随机变量和的重要性抽样

Precise Large Deviations for Sums of Independent Random Variables with Consistently Varying Tails

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