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...

Teljes leírás

Elmentve itt :
Bibliográfiai részletek
Szerzők: Oluoch Lillian Achola
Viharos László
Dokumentumtípus: Cikk
Megjelent: 2021
Sorozat: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
Leíró adatok
Tartalmi kivonat: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.
Terjedelem/Fizikai jellemzők:331-346
ISSN:2064-8316