A nonuniform bound for the approximation of Poisson binomial by Poisson distribution.
Neammanee, K. (2003)
International Journal of Mathematics and Mathematical Sciences
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Neammanee, K. (2003)
International Journal of Mathematics and Mathematical Sciences
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Adell, José A., Jodrá, P. (2006)
Journal of Inequalities and Applications [electronic only]
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Borisov, I.S. (2003)
International Journal of Mathematics and Mathematical Sciences
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M. Majsnerowska (1998)
Applicationes Mathematicae
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One more method of Poisson approximation is presented and illustrated with examples concerning binomial, negative binomial and hypergeometric distributions.
Stark, Dudley (2004)
The Electronic Journal of Combinatorics [electronic only]
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Paul Deheuvels (1985)
Trabajos de Estadística e Investigación Operativa
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We obtain in this note evaluations of the total variation distance and of the Kolmogorov-Smirnov distance between the sum of n random variables with non identical Bernoulli distributions and a Poisson distribution. Some of our results precise bounds obtained by Le Cam, Serfling, Barbour and Hall. It is shown, among other results, that if p1 = P (X1=1), ..., pn = P (Xn=1) satisfy some appropriate...
Aldona Aleškevičienė, Vytautas Statulevičius (2005)
Discussiones Mathematicae Probability and Statistics
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We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.
Steinsaltz, David (1999)
Electronic Journal of Probability [electronic only]
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Xuejun, Wang, Shuhe, Hu, Ting, Zhao, Wenzhi, Yang (2010)
Journal of Inequalities and Applications [electronic only]
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Zofia Grudzień, D. Szynal (1982)
Applicationes Mathematicae
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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....
Járai, Antal A., Kesten, Harry (2004)
Electronic Communications in Probability [electronic only]
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