A clustering law for some discrete order statistics
2003 ◽
Vol 40
(1)
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pp. 226-241
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Keyword(s):
The Law
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Let X1, X2, …, Xn be a sequence of independent, identically distributed positive integer random variables with distribution function F. Anderson (1970) proved a variant of the law of large numbers by showing that the sample maximum moves asymptotically on two values if and only if F satisfies a ‘clustering’ condition, In this article, we generalize Anderson's result and show that it is robust by proving that, for any r ≥ 0, the sample maximum and other extremes asymptotically cluster on r + 2 values if and only if Together with previous work which considered other asymptotic properties of these sample extremes, a more detailed asymptotic clustering structure for discrete order statistics is presented.
2003 ◽
Vol 40
(01)
◽
pp. 226-241
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2008 ◽
Vol 78
(7)
◽
pp. 890-895
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Keyword(s):
1970 ◽
Vol 7
(02)
◽
pp. 432-439
◽
2005 ◽
Vol 49
(4)
◽
pp. 724-734
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Keyword(s):
1965 ◽
Vol 36
(2)
◽
pp. 559-564
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Keyword(s):
2013 ◽
Vol 61
(2)
◽
pp. 161-168