Author:
De Haan Laurens,Resnick Sidney I.
Abstract
{Xn, n ≧ 1} are i.i.d. unbounded random variables with continuous d.f. F(x) =1 —e –R(x). Xj is a record value of this sequence if Xj >max {X1, …, Xj-1} The almost sure behavior of the sequence of record values {XLn} is studied. Sufficient conditions are given for lim supn→∞XLn/R–l(n)=ec, lim inf n → ∞XLn/R−1 (n) = e−c, a.s., 0 ≦ c ≦ ∞, and also for lim supn→∞ (XLn—R–1(n))/an =1, lim infn→∞ (XLn—R–1(n))/an = − 1, a.s., for suitably chosen constants an. The a.s. behavior of {XLn} is compared to that of the sequence {Mn}, where Mn = max {X1, …, Xn}. The method is to translate results for the case where the Xn's are exponential to the general case by means of an extended theory of regular variation.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference12 articles.
1. On outstanding values in a sequence of random variables
2. Von Mises R. (1936) La distribution de la plus grande de n valeurs. Selected Papers II. Amer. Math. Soc. 271–294.
3. The Rate of Growth of Sample Maxima
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