Tweedie distribution

Résumé

In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models. The Tweedie distributions were named by Bent Jørgensen after Maurice Tweedie, a statistician and medical physicist at the University of Liverpool, UK, who presented the first thorough study of these distributions in 1984. Definitions The (reproductive) Tweedie distributions are defined as subfamily of (reproductive) exponential dispersion models (ED), with a special mean-variance relationship. A random variable Y is Tweedie distributed Twp(μ,

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https://en.wikipedia.org/wiki/Tweedie_distribution

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Let X-N be an N x N random symmetric matrix with independent equidistributed entries. If the law P of the entries has a finite second moment, it was shown by Wigner [14] that the empirical distribution of the eigenvalues of X-N , once renormalized by root N, converges almost surely and in expectation to the so-called semicircular distribution as N goes to infinity. In this paper we study the same question when P is in the domain of attraction of an alpha-stable law. We prove that if we renormalize the eigenvalues by a constant a(N) of order N-1/alpha, the corresponding spectral distribution converges in expectation towards a law mu(alpha) and study some of its properties; it is a heavy-tailed probability measure which is absolutely continuous with respect to Lebesgue measure except possibly on a compact set of capacity zero.

Springer Verlag2008

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Exponential extinction time of the contact process on finite graphs

Thomas Mountford, Jean-Christophe Mourrat, Daniel Rodrigues Valesin

We study the extinction time tau of the contact process started with full occupancy on finite trees of bounded degree. We show that, if the infection rate is larger than the critical rate for the contact process on Z, then, uniformly over all trees of degree bounded by a given number, the expectation of tau grows exponentially with the number of vertices. Additionally, for any increasing sequence of trees of bounded degree, t divided by its expectation converges in distribution to the unitary exponential distribution. These results also hold if one considers a sequence of graphs having spanning trees with uniformly bounded degree, and provide the basis for powerful coarse-graining arguments. To demonstrate this, we consider the contact process on a random graph with vertex degrees following a power law. Improving a result of Chatterjee and Durrett (2009), we show that, for any non-zero infection rate, the extinction time for the contact process on this graph grows exponentially with the number of vertices. (C) 2016 Elsevier B.V. All rights reserved.

Elsevier Science Bv2016

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Measurement of the branching fractions and the invariant mass distributions for τ^{-}→h^{-}h^{+}h^{-}ν_{τ} decays

Tagir Aushev, Aurelio Bay, Sun Hee Kim, Ji Hyun Kim, Jing Li, Remi Léandre Albert Louvot, Olivier Schneider

We present a study of tau(-)->pi(-)pi(+)pi(-)nu(tau), tau(-) -> K-pi(+)pi(-)nu(tau), tau(-) -> K-K+ pi(-)nu(tau), and tau(-) -> K-K+K-nu(tau) decays using a 666 fb(-1) data sample collected with the Belle detector at the KEKB asymmetric- energy e(+)e(-) collider at and near a center- of- mass energy of 10.58 GeV. The branching fractions are measured to be B(tau(-)->pi(-)pi(+)pi(-)nu(tau)) = (8.42 +/- 0.00(-0.25)(+0.26)) x 10(-2), B(tau(-)-> K-pi(+)pi(-)nu(tau)) = 3.30 +/- 0.01(-0.17)(+0.16)) x 10(-3), B(tau(-)-> K-K+pi(-)nu(tau)) = (1.55 +/- 0.01(-0.05)(+0.06)) x 10(-3), and B(tau(-)-> K-K+K-nu(tau)), = (3.29 +/- 0.17(-0.20)(+0.19)) x 10(-5), where the first uncertainty is statistical and the second is systematic. These branching fractions do not include contributions from modes in which a pi(+)pi(-) pair originates from a K-S(0) decay. We also present the unfolded invariant mass distributions for these decays.

2010

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