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Jun 30, 2018
06/18

by
G. Afendras; N. Papadatos

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In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching problem and in a generalized matching distribution.

Topics: Probability, Mathematics

Source: http://arxiv.org/abs/1411.1165

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Sep 23, 2013
09/13

by
G. Afendras

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We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds are better than the existing ones.

Source: http://arxiv.org/abs/1110.0090v1

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93

Jul 20, 2013
07/13

by
G. Afendras; N. Papadatos; V. Papathanasiou

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For an absolutely continuous (integer-valued) r.v. $X$ of the Pearson (Ord) family, we show that, under natural moment conditions, a Stein-type covariance identity of order $k$ holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18 (2005) 237--260]). This identity is closely related to the corresponding sequence of orthogonal polynomials, obtained by a Rodrigues-type formula, and provides convenient expressions for the Fourier coefficients of an arbitrary function. Application of the...

Source: http://arxiv.org/abs/1007.3662v2

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73

Jul 20, 2013
07/13

by
G. Afendras; N. Papadatos

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Let X be an absolutely continuous random variable from the integrated Pearson family and assume that X has finite moments of any order. Equivalently, X is a linear (non-constant) transformation of Y where Y follows a Normal, a Beta or a Gamma density. Using some properties of the associate orthonormal polynomial system we provide a class of strengthened Chernoff-type variance bounds.

Source: http://arxiv.org/abs/1107.1754v3

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47

Sep 22, 2013
09/13

by
G. Afendras; N. Papadatos

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Olkin and Shepp (2005, J. Statist. Plann. Inference, vol. 130, pp. 351--358) presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincare-type and Bessel-type inequalities, for matrices of arbitrary order and for a large class of distributions.

Source: http://arxiv.org/abs/1103.5447v1

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Sep 23, 2013
09/13

by
G. Afendras; V. Papathanasiou

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We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution.

Source: http://arxiv.org/abs/1110.3265v1