caa a22 4500 605463824 CHVBK 20210128100255.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10687-015-0218-0 doi (NATIONALLICENCE)springer-10.1007/s10687-015-0218-0 Second-order properties of tail probabilities of sums and randomly weighted sums [Elektronische Daten] [Tiantian Mao, Kai Ng] 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 𝗣 ∑ 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. Springer Science+Business Media New York, 2015 Asymptotics nationallicence Hidden regular variation nationallicence Regular variation nationallicence Second-order regular variation nationallicence Mao Tiantian Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, China aut Ng Kai Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong aut Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 403-435 1386-1999 18:3<403 2015 18 10687 https://doi.org/10.1007/s10687-015-0218-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10687-015-0218-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mao Tiantian Department of Statistics and Finance, School of Management, University of Science and Technology of China, 230026, Hefei, Anhui, China aut NATIONALLICENCE 700 1- Ng Kai Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong aut NATIONALLICENCE 773 0- Extremes Springer US; http://www.springer-ny.com 18/3(2015-09-01), 403-435 1386-1999 18:3<403 2015 18 10687