NDLI: Tails of the Moments for Sums with Dominatedly Varying Random Summands

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Tails of the Moments for Sums with Dominatedly Varying Random Summands

Content Provider	MDPI
Author	Saulius, Paukštys Jonas, Šiaulys Dirma, Mantas
Copyright Year	2021
Abstract	The asymptotic behaviour of the tail expectation ? $E ({(S_{n}^{ξ})}^{α} ?_{{S_{n}^{ξ} > x}})$ is investigated, where exponent $α$ is a nonnegative real number and $S_{n}^{ξ} = ξ_{1} + \dots + ξ_{n}$ is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. It turns out that the tail expectation of such a sum can be asymptotically bounded from above and below by the sums of expectations ? $E (ξ_{i}^{α} ?_{{ξ_{i} > x}})$ with correcting constants. The obtained results are extended to the case of randomly weighted sums, where collections of random weights and primary random variables are independent. For illustration of the results obtained, some particular examples are given, where dependence between random variables is modelled in copulas framework.
Starting Page	824
e-ISSN	22277390
DOI	10.3390/math9080824
Journal	Mathematics
Issue Number	8
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-04-10
Access Restriction	Open
Subject Keyword	Mathematics Logic Tail Expectation Asymptotic Bound Quasi-asymptotic Independence Heavy-tailed Distribution Dominated Variation Copula
Content Type	Text
Resource Type	Article

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