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Natural exponential families of probability distributions and exponential-polynomial approximation
Applied Mathematics and Computation, 1993A 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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Conditional natural exponential families
Statistics & Probability Letters, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Classification of Reproducible Natural Exponential Families in the Broad Sense
Journal of Theoretical Probability, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K., Casalis, Muriel
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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 +2 more
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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 +2 more
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Natural Exponential Families and Generalized Hypergeometric Measures
Communications in Statistics - Theory and Methods, 2008Letbe 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
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A note on the discretization of natural exponential families on the real line
Metrika, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K., Letac, Gérard
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On the $q$-continuous natural exponential family
Теория вероятностей и ее примененияВ этой статье мы представляем концепцию $q$-натуральных экспоненциальных семейств в рамках $q$-исчисления, которое расширяет классическое понятие, используя $q$-ядро $e_q^{\theta x f(x)^{q-1}}$ вместо традиционного экспоненциального ядра $e^{\theta x}$.
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A new bivariate distribution in natural exponential family
Metrika, 2005We 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 ...
Masakazu Iwasaki, Hiroe Tsubaki
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Unifying the Named Natural Exponential Families and Their Relatives
The American Statistician, 2009Five 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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Inverse Natural Exponential Families on Jr
1994Abstract Recall that in Chapter 1, Section 1.4 we promised an explanation of the term ‘inverse’ appearing in the inverse Gaussian distribution. We shall now offer an explanation and justification of this usage by introducing the concept of inverse pairs of distributions (measures) and natural exponential families on R The ideas were ...
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