Results 251 to 260 of about 8,012,542 (291)

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
openaire   +1 more source

The Reconstruction of Natural Exponential Families by Their Marginals

Journal of Mathematical Sciences, 2001
Two-dimensional natural exponential families of distributions with cumulant function \(k(\theta_1,\theta_2)\) are considered. It is shown that the following relations hold \[ \begin{aligned} k(\theta_1,\theta_2) &= k_1(\theta_1+\beta_1(\theta_2))+k_2(\theta_2)- k_1(\theta_1^0+\beta_1(\theta_2))\\ &= k_2(\theta_2+\beta_2(\theta_1))+k_1(\theta_1)- k_1 ...
openaire   +2 more sources

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.
openaire   +2 more sources

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
openaire   +1 more source

Conditional natural exponential families

Statistics & Probability Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

A Classification of Reproducible Natural Exponential Families in the Broad Sense

Journal of Theoretical Probability, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K., Casalis, Muriel
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +1 more source

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.
I-Li Lu, Donald St. P. Richards
openaire   +1 more source

A note on the discretization of natural exponential families on the real line

Metrika, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K., Letac, Gérard
openaire   +2 more sources