Convergence in distribution for subset counts between random sets.
Stark, Dudley (2004)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “Moment inequalities connected with accompanying Poisson laws in Abelian groups.”
Convergence in distribution for subset counts between random sets.
Remarks on the Poisson stochastic process (III) (On a property of the homogeneous Poisson process)
C. Ryll-Nardzewski (1954)
Studia Mathematica
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The Kolmogorov distance between the binomial and Poisson laws: efficient algorithms and sharp estimates.
Adell, José A., Anoz, José M., Lekuona, Alberto (2009)
Journal of Inequalities and Applications [electronic only]
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Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
Jérôme Dedecker, Sana Louhichi (2005)
ESAIM: Probability and Statistics
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We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit....
On order statistics for random sample size having compound binomial and Poisson distributions
Zofia Grudzień, D. Szynal (1982)
Applicationes Mathematicae
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Poisson perturbations
Andrew D. Barbour, Aihua Xia (2010)
ESAIM: Probability and Statistics
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Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent...