TY - JOUR
T1 - Quantifying closeness of distributions of sums and maxima when tails are fat
AU - Willekens, E.K.E.
AU - Resnick, S.I.
PY - 1989
Y1 - 1989
N2 - Let X1, X2,…, Xn be n independent, identically distributed, non negative random variables and put and Mn = ni=1 Xi. Let (X, Y) denote the uniform distanc distributions of random variables X and Y; i.e.We consider (Sn, Mn) when P(X1>x) is slowly varying and we provide bounds for the asymptotic behaviour of this quantity as n¿8, thereby establishing a uniform rate of convergence result in Darling's law for distributions with slowly varying tails.
AB - Let X1, X2,…, Xn be n independent, identically distributed, non negative random variables and put and Mn = ni=1 Xi. Let (X, Y) denote the uniform distanc distributions of random variables X and Y; i.e.We consider (Sn, Mn) when P(X1>x) is slowly varying and we provide bounds for the asymptotic behaviour of this quantity as n¿8, thereby establishing a uniform rate of convergence result in Darling's law for distributions with slowly varying tails.
U2 - 10.1016/0304-4149(89)90038-0
DO - 10.1016/0304-4149(89)90038-0
M3 - Article
SN - 0304-4149
VL - 33
SP - 201
EP - 216
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -