Lois limites pour les statistiques d'ordre dans le cas non identiquement distribue
Mohammadine Belbachir · Canadian Journal of Statistics · 1999
Abstract Let X1, X2,… be a sequence of independent random variables with distribution functions F1, where 1 ≤ i ≤ n, and for each n ≥ 1 let X1,n ≤… ≤ Xn,n denote the order statistics of the first n random variables. Under suitable hypotheses about the F1, we characterize the limit distribution functions H(x) for which P(Xk,n ⩽ anx + bn) → H(x), where an > 0 and bn are real constants. We consider the cases where κ = κ(n) satisfies √n {κ(n)/n — λ} → 0 and √n {κ(n)/n — λ} → ∞ separately.