Results 221 to 230 of about 175,990 (247)

The Lindsay transform of natural exponential families

Canadian Journal of Statistics, 1994
AbstractLet μ be an infinitely divisible positive measure on R. If the measure ρμ is such that x‐2[ρμ(dx)—ρμ({0})δ0(dx)] is the Lévy measure associated with μ and is infinitely divisible, we consider for all positive reals α and β the measure Tα,β(μ) which is the convolution of μ*α and ρμ*β.
Kokonendji, C. C., Seshadri, V.
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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.
I-Li Lu, Donald St. P. Richards
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Haight's distributions as a natural exponential family

Statistics & Probability Letters, 1988
In an index to the distributions of mathematical statistics, \textit{F. A. Haight} [J. Res. Nat. Bureau of Standards 65B(1), 23-60 (1961)] considers, without giving any references, the following distribution: \[ \alpha^{-1}\exp (-xe^{\alpha}\alpha^{- 1})\sum^{\infty}_{n=0}(n+1)^{n-1}(n!)^{-2}x^ n\mathbf{1}_{(0,\infty)}(x)dx\quad for\quad ...
Letac, Gérard, Seshadri, V.
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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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HEISENBERG–WEYL LIE ALGEBRA AND NATURAL EXPONENTIAL FAMILIES

Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2007
We present in this work a specific construction of raising and lowering operators for 2-orthogonal quasi-monomial polynomials associated with continuous and discrete natural exponential families. We use these operators in order to characterize the real class of cubic natural exponential families.
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Conditionally Reducible Natural Exponential Families and Enriched Conjugate Priors

Scandinavian Journal of Statistics, 2001
Consider a standard conjugate family of prior distributions for a vector‐parameter indexing an exponential family. Two distinct model parameterizations may well lead to standard conjugate families which are not consistent, i.e. one family cannot be derived from the other by the usual change‐of‐variable technique.
G. CONSONNI, VERONESE, PIERO
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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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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 ...
Masakazu Iwasaki, Hiroe Tsubaki
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Inverse Natural Exponential Families on Jr

1994
Abstract 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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