scholarly journals On the Functional Central Limit Theorem for the Ewens Sampling Formula

1991 ◽  
Vol 1 (4) ◽  
pp. 539-545 ◽  
Author(s):  
Peter Donnelly ◽  
Thomas G. Kurtz ◽  
Simon Tavare
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Functional Central Limit Theorem ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Functional Central Limit

A functional central limit theorem for the Ewens sampling formula

1990 ◽  
Vol 27 (1) ◽  
pp. 28-43 ◽  
Author(s):  
Jennie C. Hansen
Keyword(s):  
Population Genetics ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Step Function ◽  
Frequency Limit ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Partition Structure ◽  
Functional Central Limit

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.

A functional central limit theorem for the Ewens sampling formula

1990 ◽  
Vol 27 (01) ◽  
pp. 28-43 ◽  
Author(s):  
Jennie C. Hansen
Keyword(s):  
Population Genetics ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Step Function ◽  
Frequency Limit ◽  
Ewens Sampling Formula ◽  
Sampling Formula ◽  
Partition Structure ◽  
Functional Central Limit

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.

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