Second-order properties of tail probabilities of sums and randomly weighted sums
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| 024 | 7 | 0 | |a 10.1007/s10687-015-0218-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10687-015-0218-0 | ||
| 245 | 0 | 0 | |a Second-order properties of tail probabilities of sums and randomly weighted sums |h [Elektronische Daten] |c [Tiantian Mao, Kai Ng] |
| 520 | 3 | |a Let X 1, ... , X n be independent nonnegative random variables with respective survival functions F ¯ 1 , ... , F ¯ n $\overline {F}_{1}, \ldots , \overline {F}_{n}$ , and let Θ1, ... , Θ n be (not necessarily independent) nonnegative random variables, independent of X 1, ... , X n , satisfying certain moment conditions. This paper consists of two parts. In the first part, we investigate second-order expansions of ∑ i = 1 n X i > t $ \left ({\sum }^{n}_{i=1} X_{i}>t\right )$ as t → ∞ $t\to {\infty }$ under the assumption that the F ¯ i $\overline {F}_{i}$ are of second-order regular variation (2RV) with the same first-order index but with different second-order indexes. In the second part, under the assumption that the F ¯ 1 = ⋯ = F ¯ n $\overline {F}_{1}=\cdots =\overline {F}_{n}$ have 2RV tails, second-order expansions of tail probabilities of the randomly weighted sum ∑ i = 1 n Θ i X i ${\sum }^{n}_{i=1} {\Theta }_{i} X_{i}$ are studied. The closure property of 2RV under randomly weighted sum is also discussed. The main results in this paper generalize and strengthen several known results in the literature. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 690 | 7 | |a Asymptotics |2 nationallicence | |
| 690 | 7 | |a Hidden regular variation |2 nationallicence | |
| 690 | 7 | |a Regular variation |2 nationallicence | |
| 690 | 7 | |a Second-order regular variation |2 nationallicence | |
| 700 | 1 | |a Mao |D Tiantian |u Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, China |4 aut | |
| 700 | 1 | |a Ng |D Kai |u Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |4 aut | |
| 773 | 0 | |t Extremes |d Springer US; http://www.springer-ny.com |g 18/3(2015-09-01), 403-435 |x 1386-1999 |q 18:3<403 |1 2015 |2 18 |o 10687 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10687-015-0218-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10687-015-0218-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mao |D Tiantian |u Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ng |D Kai |u Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Extremes |d Springer US; http://www.springer-ny.com |g 18/3(2015-09-01), 403-435 |x 1386-1999 |q 18:3<403 |1 2015 |2 18 |o 10687 | ||