Asymptotic distributions for weighted power sums of extreme values
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 pos...
Saved in:
| Main Authors: | |
|---|---|
| Format: | Article |
| Published: |
2021
|
| Series: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-323-9 |
| Online Access: | http://acta.bibl.u-szeged.hu/73932 |
| LEADER | 01347nab a2200217 i 4500 | ||
|---|---|---|---|
| 001 | acta73932 | ||
| 005 | 20211116095137.0 | ||
| 008 | 211116s2021 hu o 0|| eng d | ||
| 022 | |a 2064-8316 | ||
| 024 | 7 | |a 10.14232/actasm-020-323-9 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Oluoch Lillian Achola | |
| 245 | 1 | 0 | |a Asymptotic distributions for weighted power sums of extreme values |h [elektronikus dokumentum] / |c Oluoch Lillian Achola |
| 260 | |c 2021 | ||
| 300 | |a 331-346 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 87 No. 1-2 | |
| 520 | 3 | |a 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. | |
| 695 | |a Matematika | ||
| 700 | 0 | 1 | |a Viharos László |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/73932/1/math_087_numb_001-002_331-346.pdf |z Dokumentum-elérés |