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OPTIMAL UNBIASED MEANS, POLYNOMIAL MOMENT RELATIONS, AND NATURAL EXPONENTIAL FAMILIES
Statistics & Risk Modeling, 1996Summary: Assume that a statistical model \({\mathcal P}\) on the real line possesses moments of every order and is such that, for some positive integer \(k\), the moment of order \(k+1\) is a polynomial function \(p\) of the \(k\) moments of lower order. Then the UMVU-property of the sample mean in a corresponding IID-model implies that \({\mathcal P}\)
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Parameterizations for Natural Exponential Families with Quadratic Variance Functions
Journal of the American Statistical Association, 1994Abstract Parameterizations for natural exponential families (NEF's) with quadratic variance functions (QVF's) are compared according to the nearness to normality of the likelihood and posterior distribution. Nonnormality of the likelihood (posterior) is measured using two criteria.
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Real natural exponential families and generalized orthogonality
Communications in Statistics - Theory and Methods, 2023Raouf Fakhfakh, Marwa Hamza
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IEEE International Conference on Systems, Man and Cybernetics, 2012
Taher Ben Arab, M. Zribi, A. Masmoudi
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Taher Ben Arab, M. Zribi, A. Masmoudi
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Functionally compatible local characteristics for some natural conjugate exponential families
2007The local specification of priors in nondecomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma (conjugate prior for Poisson counts) and the Wishart distribution (conjugate ...
ASCI, CLAUDIO, MAURO PICCIONI
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Quantifying Prior Opinion in Length-Biased Linear Mean Natural Exponential Family
, 1992R. Shanmugam
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