Abstract
We consider the random number of (Griffiths-Engen-McCloskey (GEM))-(Poisson-Dirichlet) components which are greater than ε. In two alternative and similar ways, letting Dirichlet laws and Ewens sampling formula laws respectively converge to the GEM-(Poisson-Dirichlet) law and using the Stein-Chen coupling method, we prove the Poisson approximation with respect to the total variation metric of the satisfactory order of magnitude 1/expectation.
Citation
Ulrich Martin Hirth. "A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method." Bernoulli 3 (2) 225 - 232, June 1997.
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