Oluoch Lillian Achola and Viharos László: Asymptotic distributions for weighted power sums of extreme values. In: Acta scientiarum mathematicarum, (87) 1-2. pp. 331-346. (2021)
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Abstract
Let X1,n ≤ · · · ≤ Xn,n be the order statistics of n independent random variables with a common distribution function F having right heavy tail with tail index γ. Given known constants di,n, 1 ≤ i ≤ n, consider the weighted power sums Pkn i=1 dn+1−i,n logp Xn+1−i,n, where p > 0 and the kn are positive integers such that kn → ∞ and kn/n → 0 as n → ∞. Under some constraints on the weights di,n, we prove asymptotic normality for the power sums over the whole heavy-tail model. We apply the obtained result to construct a new class of estimators for the parameter γ.
| Item Type: | Article |
|---|---|
| Heading title: | Probability theory |
| Journal or Publication Title: | Acta scientiarum mathematicarum |
| Date: | 2021 |
| Volume: | 87 |
| Number: | 1-2 |
| ISSN: | 2064-8316 |
| Page Range: | pp. 331-346 |
| Language: | English |
| Related URLs: | http://acta.bibl.u-szeged.hu/73791/ |
| DOI: | 10.14232/actasm-020-323-9 |
| Uncontrolled Keywords: | Matematika |
| Additional Information: | Bibliogr.: p. 345-346. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 16. 09:50 |
| Last Modified: | 2021. Nov. 16. 09:51 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73932 |
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