Results 211 to 220 of about 54,704 (250)

Predictive Fit for Natural Exponential Families

Biometrika, 1989
The basic problem considered is where the observed data are all realizations of a random variable X and some probability statement about a future variable from the same distribution is desired. The paper examines such predictions with regard to a particular measure of prediction fit, the average Kullback-Leibler divergence between distributions.
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Conjugate Parameterizations for Natural Exponential Families

Journal of the American Statistical Association, 1995
Abstract Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this
E. Gutiérrez-Peña, A. F. M. Smith
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Conditional natural exponential families

Statistics & Probability Letters, 2006
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Natural exponential families of probability distributions and exponential-polynomial approximation

Applied Mathematics and Computation, 1993
A Dirichlet polynomial in a finite linear combination of the functions \(e^{\lambda_ k x}, e^{\lambda_ k x},\dots, x^{m_ k-1} e^{\lambda_ k x}\), \(k=1,2,3,\dots\), where \(\{\lambda_ k\}\) is a sequence of complex numbers and \(\{m_ k\}\) is a sequence of positive integers. The authors [Appl. Math. Comput. 53, No.
Martin, Clyde, Shubov, Victor
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A Classification of Reproducible Natural Exponential Families in the Broad Sense

Journal of Theoretical Probability, 2003
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Bar-Lev, Shaul K., Casalis, Muriel
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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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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 ...
Aida Jarraya, Philippe Leray 0001, Afif Masmoudi   +2 more
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The diagonal multivariate natural exponential families and their classification

Journal of Theoretical Probability, 1994
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Bar-Lev, Shaul K., Bshouty, Daoud, Enis, Peter, Letac, Gérard, Lu, I- Li, Richards, Donald   +5 more
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Unifying the Named Natural Exponential Families and Their Relatives

The American Statistician, 2009
Five of the six univariate natural exponential families (NEFs) with quadratic variance functions (QVFs), meaning that their variances are at most quadratic functions of their means, are the Normal, Poisson, Gamma, Binomial, and Negative Binomial distributions.
Morris, Carl N., Lock, Kari F.
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