NDLI: Second-order properties of tail probabilities of sums and randomly weighted sums

Content Provider	Springer Nature Link
Author	Mao, Tiantian Ng, Kai Wang
Copyright Year	2015
Abstract	Let X 1, … , X n be independent nonnegative random variables with respective survival functions $\overline {F}_{1}, \ldots , \overline {F}_{n}$ , 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 $ \left ({\sum }^{n}_{i=1} X_{i}>t\right )$ as $t\to {\infty }$ under the assumption that the $\overline {F}_{i}$ 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 $\overline {F}_{1}=\cdots =\overline {F}_{n}$ have 2RV tails, second-order expansions of tail probabilities of the randomly weighted sum ${\sum }^{n}_{i=1} {\Theta }_{i} X_{i}$ 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.
Starting Page	403
Ending Page	435
Page Count	33
File Format	PDF
ISSN	13861999
Journal	Extremes
Volume Number	18
Issue Number	3
e-ISSN	1572915X
Language	English
Publisher	Springer US
Publisher Date	2015-06-06
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asymptotics Hidden regular variation Regular variation Second-order regular variation Statistics Quality Control, Reliability, Safety and Risk Civil Engineering Hydrogeology Environmental Management Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics, Econometrics and Finance Engineering

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