A functional central limit theorem for the Ewens sampling formula
1990 ◽
Vol 27
(01)
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pp. 28-43
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Keyword(s):
For each n > 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n. To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, we associate to each partition a step function on [0, 1]. Each jump in the function equals the number of parts in the partition of a certain size. We normalize these functions and show that the induced measures on D[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition structure.
1991 ◽
Vol 1
(4)
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pp. 539-545
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Keyword(s):
2007 ◽
Vol 117
(8)
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pp. 1137-1164
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1993 ◽
Vol 44
(2)
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pp. 314-320
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1981 ◽
Vol 25
(4)
◽
pp. 667-688
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2016 ◽
Vol 26
(6)
◽
pp. 3659-3698
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