On the relationship between convergence in distribution and convergence of expected extremes
Authors:
Theodore P. Hill and M. C. Spruill
Journal:
Proc. Amer. Math. Soc. 121 (1994), 12351243
MSC:
Primary 60F99; Secondary 60G70
Erratum:
Proc. Amer. Math. Soc. 128 (2000), 625626.
MathSciNet review:
1195722
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Abstract 
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Abstract: It is well known that the expected values , of the kmaximal order statistics of an integrable random variable X uniquely determine the distribution of X. The main result in this paper is that if , is a sequence of integrable random variables with for all , then there exists a random variable X with for all and if and only if , in which case the collection is also uniformly integrable. In addition, it is shown using a theorem of Müntz that any subsequence , satisfying uniquely determines the law of X.
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 , Probability and measure, 2nd ed., Wiley, New York, 1986. MR 830424 (87f:60001)
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 J. Galambos, The asymptotic theory of extreme order statistics, Wiley, New York, 1978. MR 489334 (80b:60040)
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 C. Müntz, Über den approximationssatz von Weierstrass, SchwartzFestschrift, 1914.
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 I. Natanson, Constructive function theory, Vol. II, Fredrick Ungar, New York, 1965.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199411957229
PII:
S 00029939(1994)11957229
Keywords:
Convergence in distribution,
convergence of expected extremes,
maximal order statistics,
Müntz's theorem,
extreme valuetheory
Article copyright:
© Copyright 1994
American Mathematical Society
