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On standard conjugate families for natural exponential families with bounded natural parameter space. [PDF]
J Multivar Anal, 2014 Diaconis and Ylvisaker (1979) give necessary conditions for conjugate priors for distributions from the natural exponential family to be proper as well as to have the property of linear posterior expectation of the mean parameter of the family. Their conditions for propriety and linear posterior expectation are also sufficient if the natural parameter ...
Hornik K, Grün B.
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On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families
Mathematics, 2021 Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
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Extended Divergence on a Foliation by Continuous-Type Escort Distributions [PDF]
EntropyFrom an information geometric perspective, this study considers a natural foliation of dualistic structures associated with escort distributions of exponential families.
Keiko Uohashi
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Natural Exponential Families with Quadratic Variance Functions
Annals of Statistics, 1982 The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions (the variance is at most a quadratic function of the mean). Only one other such family exists. Much theory is unified for these six natural exponential families by appeal to their quadratic variance ...
Carl N Morris
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Information Geometry and Asymptotic Theory for SMML Estimators [PDF]
EntropyStrict minimum message length (SMML) is an information-theoretic coding principle that represents a continuous statistical model by a finite set of assertions and a partition of the sample space.
Enes Makalic, Daniel F. Schmidt
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A new variance estimation in natural exponential families
Research in StatisticsThis article focuses on improving the estimation of population variances for natural exponential family distributions, drawing inspiration from the innovative idea presented by Stein.
Arampamoorthy Laheetharan +1 more
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Natural Exponential Families with Quadratic Variance Functions: Statistical Theory
Annals of Statistics, 1983 The normal, Poisson, gamma, binomial, negative binomial, and NEFGHS distributions are the six univariate natural exponential families (NEF) with quadratic variance functions (QVF). This sequel to Morris (1982) treats certain statistical topics that can be handled within this unified NEF-QVF formulation, including unbiased estimation, Bhattacharyya and ...
Carl N Morris
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Mathematics, 2023 The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for modeling skewed ...
Shaul K. Bar-Lev
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Exponential Families with External Parameters
Entropy, 2022 In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters.
Marco Favretti
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Flavor non-universal Pati-Salam unification and neutrino masses
Physics Letters B, 2021 We analyze the neutrino mass spectrum and discuss the extra-dimensional interpretation of a three-site Pati-Salam model which i) unifies all families of quark and leptons, ii) provides a natural description of the Standard Model Yukawa couplings, iii ...
Javier Fuentes-Martín +3 more
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