scholarly journals Stein’s method for the Poisson–Dirichlet distribution and the Ewens sampling formula, with applications to Wright–Fisher models

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Han L. Gan ◽  
Nathan Ross
Keyword(s):  
Dirichlet Distribution ◽  
Stein’S Method ◽  
Stein's Method ◽  
Ewens Sampling Formula ◽  
Sampling Formula

scholarly journals Gaussian Limits Associated with the Poisson-Dirichlet Distribution and the Ewens Sampling Formula

2002 ◽  
Vol 12 (1) ◽  
pp. 101-124 ◽  
Author(s):  
Paul Joyce ◽  
Stephen M. Krone ◽  
Thomas G. Kurtz
Keyword(s):  
Dirichlet Distribution ◽  
Ewens Sampling Formula ◽  
Sampling Formula

On the rate of Poisson process approximation to a Bernoulli process

1997 ◽  
Vol 34 (4) ◽  
pp. 898-907 ◽  
Author(s):  
Aihua Xia
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Discrete Time ◽  
Wasserstein Distance ◽  
Stein’S Method ◽  
Upper Bounds ◽  
Stein's Method ◽  
Bernoulli Process ◽  
Logarithmic Factor ◽  
Process Approximation

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbour et al. (1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.

STEIN'S METHOD AND THE BERRY-ESSÉEN THEOREM

1984 ◽  
Vol 26 (1) ◽  
pp. 8-15 ◽  
Author(s):  
A. D. Barbour ◽  
Peter Hall
Keyword(s):  
Stein’S Method ◽  
Stein's Method
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