Bero Roos
University of Hamburg
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Featured researches published by Bero Roos.
Theory of Probability and Its Applications | 2001
Bero Roos
The Poisson binomial distribution is approximated by a binomial distribution and also by finite signed measures resulting from the corresponding Krawtchouk expansion. Bounds and asymptotic relations for the total variation distance and the point metric are given.
Bernoulli | 1999
Bero Roos
The Poisson-binomial distribution is approximated by a Poisson law with respect to a new multimetric (difference metric) unifying a broad class of probability metrics between discrete distributions. The accompanying non-metric situation is also considered leading to moderateand large-deviation results. Using the Charlier B expansion and Fourier arguments, sharp bounds and asymptotic relations are given.
Statistics & Probability Letters | 2001
Bero Roos
We present some new sharp bounds for several distances between the Poisson binomial distribution and the Poisson law with the same mean. It is shown that the constants involved cannot be reduced.
Journal of Statistical Planning and Inference | 2003
Bero Roos
We consider the approximation of mixed Poisson distributions by Poisson laws and also by related finite signed measures of higher order. Upper bounds and asymptotic relations are given for several distances. Even in the case of the Poisson approximation with respect to the total variation distance, our bounds have better order than those given in the literature. In particular, our results hold under weaker moment conditions for the mixing random variable. As an example, we consider the approximation of the negative binomial distribution, which enables us to prove the sharpness of a constant in the upper bound of the total variation distance. The main tool is an integral formula for the difference of the counting densities of a Poisson distribution and a related finite signed measure.
Theory of Probability and Its Applications | 2003
Bero Roos
The generalized multinomial distribution is approximated by finite signed measures, resulting from a Poisson-type expansion in the exponent. In the univariate case, this expansion was first used by Kornya and Presman. We apply Kerstans method and present a bound for the total variation distance with explicit constants.
Theory of Probability and Its Applications | 1999
Bero Roos
The aim of this paper is to introduce the multivariate Charlier B expansion to the metric multivariate Poisson approximation of a generalized multinomial distribution considered by Barbour [J. Appl. Probab., 25 (1988), pp. 175--184] and Deheuvels and Pfeifer [J. Multivariate Anal., 25 (1988), pp. 65--89]. Bounds for the total variation and the point metric are given.
Theory of Probability and Its Applications | 2002
Bero Roos
The generalized multinomial distribution is approximated by multinomial distributions and also by finite signed measures resulting from the corresponding multivariate Krawtchouk expansion. Bounds for the total variation norm and the
Theory of Probability and Its Applications | 2004
Bero Roos
\ell_\infty
Statistics & Probability Letters | 1995
Bero Roos
-norm are presented. The method used is a multivariate extension of that in~[B.~Roos, Theory Probab. Appl., 45 (2000), pp. 258--272], although additional complications occur.
Bernoulli | 2010
Bero Roos
We present an upper bound for the total variation distance between the generalized polynomial distribution and a finite signed measure, which is the convolution of two finite signed measures, one of which is of Kornya--Presman type. In the one-dimensional Poisson case, such a finite signed measure was first considered by K. Borovkov and D. Pfeifer [{\em J. Appl.\ Probab.}, 33 (1996), pp. 146--155].We give asymptotic relations in the one-dimensional case, and, as an example, the independent identically distributed record model is investigated.It turns out that here the approximation is of order