Representations and limit theorems for extreme value distributions
- 1 September 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (3) , 639-644
- https://doi.org/10.2307/3213128
Abstract
Let Xn1 ≦ Xn2 ≦ ··· ≦ Xnn denote the order statistics from a sample of n independent, identically distributed random variables, and suppose that the variables Xnn, Xn, n–1, ···, when suitably normalized, have a non-trivial limiting joint distribution ξ1, ξ2, ···, as n → ∞. It is well known that the limiting distribution must be one of just three types. We provide a canonical representation of the stochastic process {ξn, n ≧ 1} in terms of exponential variables, and use this representation to obtain limit theorems for ξ n as n →∞.Keywords
This publication has 7 references indexed in Scilit:
- On central limit and iterated logarithm supplements to the martingale convergence theoremJournal of Applied Probability, 1977
- Convergence in distribution of quotients of order statisticsStochastic Processes and their Applications, 1975
- Tail sums of convergent series of independent random variablesMathematical Proceedings of the Cambridge Philosophical Society, 1974
- The structure of extremal processesAdvances in Applied Probability, 1973
- Extremal Processes, IIIllinois Journal of Mathematics, 1966
- On the theory of order statisticsActa Mathematica Hungarica, 1953
- Sur La Distribution Limite Du Terme Maximum D'Une Serie AleatoireAnnals of Mathematics, 1943