The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Jean-renaud Pycke - One of the best experts on this subject based on the ideXlab platform.
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on a generalization of the renyi srivastava characterization of the Poisson Law
Journal of Applied Probability, 2021Co-Authors: Jean-renaud PyckeAbstract:We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson Law due to Renyi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.
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On a generalization of the Rényi–Srivastava characterization of the Poisson Law
Journal of Applied Probability, 2021Co-Authors: Jean-renaud PyckeAbstract:We give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson Law due to Renyi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.
Alberto Lekuona - One of the best experts on this subject based on the ideXlab platform.
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sharp bounds on the entropy of the Poisson Law and related quantities
IEEE Transactions on Information Theory, 2010Co-Authors: José A. Adell, Alberto LekuonaAbstract:One of the difficulties in calculating the capacity of certain Poisson channels is that H(?), the entropy of the Poisson distribution with mean ?, is not available in a simple form. In this paper, we derive upper and lower bounds for H(?) that are asymptotically tight and easy to compute. The derivation of such bounds involves only simple probabilistic and analytic tools. This complements the asymptotic expansions of Knessl (1998), Jacquet and Szpankowski (1999), and Flajolet (1999). The same method yields tight bounds on the relative entropy D(n, p) between a binomial and a Poisson, thus refining the work of Harremoe?s and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.
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Sharp Bounds on the Entropy of the Poisson Law and Related Quantities
IEEE Transactions on Information Theory, 2010Co-Authors: José A. Adell, Alberto LekuonaAbstract:One of the difficulties in calculating the capacity of certain Poisson channels is that H(lambda), the entropy of the Poisson distribution with mean lambda, is not available in a simple form. In this work we derive upper and lower bounds for H(lambda) that are asymptotically tight and easy to compute. The derivation of such bounds involves only simple probabilistic and analytic tools. This complements the asymptotic expansions of Knessl (1998), Jacquet and Szpankowski (1999), and Flajolet (1999). The same method yields tight bounds on the relative entropy D(n, p) between a binomial and a Poisson, thus refining the work of Harremoes and Ruzankin (2004). Bounds on the entropy of the binomial also follow easily.
Benoît Saussol - One of the best experts on this subject based on the ideXlab platform.
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Poisson Law for some non uniformly hyperbolic dynamical systems with polynomial rate of mixing
Ergodic Theory and Dynamical Systems, 2016Co-Authors: Françoise Pene, Benoît SaussolAbstract:We consider some nonuniformly hyperbolic invertible dynamical systems which are modeled by a Gibbs-Markov-Young tower. We assume a polynomial tail for the inducing time and a polynomial control of hyperbolicity, as introduced by Alves, Pinheiro and Azevedo. These systems admit a physical measure with polynomial rate of mixing. In this paper we prove that the distribution of the number of visits to a ball B(x, r) converges to a Poisson distribution as the radius r → 0 and after suitable normalization.
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Poisson Law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing
2014Co-Authors: Françoise Pene, Benoît SaussolAbstract:We consider some nonuniformly hyperbolic invertible dynamical systems which are modeled by a Gibbs-Markov-Young tower. We assume a polynomial tail for the inducing time and a polynomial control of hyperbolicity, as introduced by Alves, Pinheiro and Azevedo. These systems admit a physical measure with polynomial rate of mixing. In this paper we prove that the distribution of the number of visits to a ball B(x, r) converges to a Poisson distribution as the radius r → 0 and after suitable normalization.
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Statistics of Return Times:¶A General Framework and New Applications
Communications in Mathematical Physics, 1999Co-Authors: Masaki Hirata, Benoît Saussol, Sandro VaientiAbstract:In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the K th return time (suitably rescaled) and the Poisson Law for measurable dynamical systems. In the case that the system exhibits strong mixing properties, these bounds are explicitly expressed in terms of the speed of mixing. Using these approximations, the Poisson Law is finally proved to hold for a large class of non hyperbolic systems on the interval.
Bero Roos - One of the best experts on this subject based on the ideXlab platform.
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Sharp constants in the Poisson approximation
Statistics & Probability Letters, 2001Co-Authors: Bero RoosAbstract: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.
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asymptotics and sharp bounds in the Poisson approximation to the Poisson binomial distribution
Bernoulli, 1999Co-Authors: Bero RoosAbstract: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.
Sandro Vaienti - One of the best experts on this subject based on the ideXlab platform.
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Statistics of Return Times:¶A General Framework and New Applications
Communications in Mathematical Physics, 1999Co-Authors: Masaki Hirata, Benoît Saussol, Sandro VaientiAbstract:In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the K th return time (suitably rescaled) and the Poisson Law for measurable dynamical systems. In the case that the system exhibits strong mixing properties, these bounds are explicitly expressed in terms of the speed of mixing. Using these approximations, the Poisson Law is finally proved to hold for a large class of non hyperbolic systems on the interval.