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Record values and extreme value distributions

Published online by Cambridge University Press:  14 July 2016

H. N. Nagaraja
H. N. Nagaraja*
Affiliation:
The Ohio State University
*
∗Postal address: 128 Cockins Hall, 1958 Neil Avenue, Columbus, OH 43210, U.S.A.
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Abstract

The limit distribution of the k th maximum from a random sample of size n when n → ∞ is identified as the distribution of the k th lower record value from one of three extreme value distributions. This fact is used in giving a different canonical representation and new proofs of the results of Hall (1978) for this limiting random variable. A characterization of the exponential distribution based on upper record values is given.

Keywords

MULTIVARIATE EXTREMAL DISTRIBUTIONRECORD VALUESCHARACTERIZATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 233 - 239
Copyright
Copyright © Applied Probability Trust 1982 

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References

Chandler, K. N. (1952) The distribution and frequency of record values. J. R. Statist. Soc. B 14, 220–228.Google Scholar
Dwass, M. (1966) Extremal processes II. Illinois J. Math. 10, 381–391.CrossRefGoogle Scholar
Gnedenko, B. V. (1943) Sur la distribution limite du terme maximum d'une série aléatoire. Ann. Math. (2) 44, 423–453.CrossRefGoogle Scholar
Hall, P. (1978) Representations and limit theorems for extreme value distributions. J. Appl. Prob. 15, 639–644.CrossRefGoogle Scholar
Lamperti, J. (1964) On extreme order statistics. Ann. Math. Statist. 35, 1726–1737.CrossRefGoogle Scholar
Rao, C. R. (1973) Linear Statistical Inference and its Applications, 2nd edn. Wiley, New York.CrossRefGoogle Scholar
Resnick, S. I. (1973) Limit laws for record values. Stoch. Proc. Appl. 1, 67–82.CrossRefGoogle Scholar
Shorrock, R. W. (1972) A limit theorem for inter-record times. J. Appl. Prob. 9, 219–223.CrossRefGoogle Scholar
Srivastava, R. C. (1978) Some characterizations of the exponential distribution based on record values. Ohio State U. Statistics Technical Report No. 170.Google Scholar
Tata, M. N. (1969) On outstanding values in a sequence of random variables. Z. Wahrscheinlichkeitsth. 12, 9–20.CrossRefGoogle Scholar
Weissman, I. (1975) Multivariate extremal processes generated by independent non-identically distributed random variables. J. Appl. Prob. 12, 477–487.CrossRefGoogle Scholar
Weissman, I. (1978) Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc. 73, 812–815.Google Scholar