Results 201 to 210 of about 544,925 (236)

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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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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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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Online Density Estimation of Nonstationary Sources Using Exponential Family of Distributions

IEEE Transactions on Neural Networks and Learning Systems, 2018
We investigate online probability density estimation (or learning) of nonstationary (and memoryless) sources using exponential family of distributions. To this end, we introduce a truly sequential algorithm that achieves Hannan-consistent log-loss regret
Kaan Gokcesu, S. Kozat
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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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