Results 261 to 270 of about 396,333 (302)

Orthogonal polynomials and natural exponential families

Test, 1996
There exist several different characterizations of the class of quadratic natural exponential families onR, two of which use orthogonal polynomials. In Feinsilver (1986), the polynomials result from the derivation of the probability densities while Meixner (1934) adopts an exponential generating function.
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Natural Exponential Families and Generalized Hypergeometric Measures

Communications in Statistics - Theory and Methods, 2008
Letbe a positive Borel measure on R n and pFq(a1,... ,ap;b1,... ,bq;s) be a generalized hypergeometric series. We define a generalized hypergeomet- ric measure, µp,q := pFq(a1,... ,ap;b1,... ,bq; ), as a series of convolution powers of the measure , and we investigate classes of probability distri- butions which are expressible as such a measure.
Donald St. P. Richards, I-Li Lu
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A new bivariate distribution in natural exponential family

Metrika, 2005
We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability ...
Hiroe Tsubaki, Masakazu Iwasaki
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Finite mixtures of natural exponential families

Canadian Journal of Statistics, 1991
Let μ be a positive measure concentrated on R+ generating a natural exponential family (NEF) F with quadratic variance function VF(m), m being the mean parameter of F. It is shown that v(dx) = (γ+x)μ(γ ≥ 0) (γ ≥ 0) generates a NEF G whose variance function is of the form l(m)Δ+cΔ(m), where l(m) is an affine function of m, Δ(m) is a polynomial in m (the
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Discrete Exponential Bayesian Networks: An Extension of Bayesian Networks to Discrete Natural Exponential Families

2011 IEEE 23rd International Conference on Tools with Artificial Intelligence, 2011
In this paper, we develop the notion of discrete exponential Bayesian network, parametrization of Bayesian networks (BNs) using more general discrete quadratic exponential families instead of usual multinomial ones. We then introduce a family of prior distributions which generalizes the Dirichlet prior classically used with discrete Bayesian network ...
Jarraya, Aida, Leray, Philippe, Masmoudi, Afif   +2 more
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Trace of the Variance-Covariance Matrix in Natural Exponential Families

Communications in Statistics - Theory and Methods, 2015
In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs.
Taher Ben Arab, Afif Masmoudi, Mourad Zribi   +2 more
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On Lévy measures for infinitely divisible natural exponential families

Statistics & Probability Letters, 2006
Abstract We link the infinitely divisible measure μ to its modified Levy measure ρ = ρ ( μ ) in terms of their variance functions, where x - 2 [ ρ ( d x ) - ρ ( { 0 } ) δ 0 ( d x ) ] is the Levy measure associated with μ . We deduce that, if the variance function of μ is a polynomial
Célestin C. Kokonendji, Mohamed Khoudar
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Limit distributions of unbiased estimators in natural exponential families

Statistics, 2002
We obtain the possible limit distributions of unbiased estimators of functions of the parameter of a natural exponential family. The limit distribution depends on j , the order of the first non-zero derivative at the true (but usually unknown) value of the parameter.
F. Lo´pez-Bla´zquez, B. Salamanca-Miño   +1 more
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Natural exponential families associated to Pick functions

Test, 1998
We define a quadratic action of the group of invertible (2,2) matrices of determinant 1 by Mœbius transformsh(x)=(ax+b)/(cx+d) on the natural exponential families (NEF) on ℝ which changes the mean functionk′ of the NEFF in the new mean functionh(k′) associated to the new NEF, denoted byh(F). The variance function ofh(F) is(cm+d)2VF(h(m)).
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Posterior variance for quadratic natural exponential families

Statistics & Probability Letters, 2001
Within the framework of the quadratic natural exponential families we construct a basis of polynomials orthogonal with respect to the posterior density. This construction is adapted from Walter and Hamedani (Ann. Statist. 3 (1991) 1191) and we exploit them to establish lower bounds for the posterior variance.
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