A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method
Martin Hirth, Ulrich
Bernoulli, Tome 3 (1997) no. 3, p. 225-232 / Harvested from Project Euclid
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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.
Publié le : 1997-06-14
Classification:  coupling,  Dirichlet distribution,  Ewens sampling formula,  GEM distribution,  Poisson approximation,  Poisson-Dirichlet distribution,  Stein-Chen method,  total variation metric 
@article{1177526730,
     author = {Martin Hirth, Ulrich},
     title = {A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method},
     journal = {Bernoulli},
     volume = {3},
     number = {3},
     year = {1997},
     pages = { 225-232},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177526730}
}

Martin Hirth, Ulrich. A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method. Bernoulli, Tome 3 (1997) no. 3, pp.  225-232. http://gdmltest.u-ga.fr/item/1177526730/