Characterization of the Jørgensen set in generalized linear models

DOI10.1007/BF02562678zbMath0815.62030OpenAlexW2015410216MaRDI QIDQ1343683

Gérard Letac, Muriel Casalis

Publication date: 30 January 1995

Published in: Test (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02562678

zbMATH Keywords

Hermitian matricesquaternionsnatural exponential familysymmetric conesWishart distributionsnormal distributionsinverse Gaussian distributionsgeneral exponential familiesJorgensen set

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Generalized linear models (logistic models) (62J12) Distribution theory (60E99)

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Cites Work

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• Proof of a conjecture of M.L. Eaton on the characteristic function of the Wishart distribution
• Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)
• A characterization of the Wishart exponential families by an invariance property
• Invariant generalized functions in homogeneous domains
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Invariant normal models
• A decomposition for the exponential dispersion model generated by the invariance measure on the hyperboloid
• On an algebraic generalization of the quantum mechanical formalism
• Function spaces and reproducing kernels on bounded symmetric domains
• A Characterization of the Wishart Distribution
• The Analytic Continuation of the Discrete Series.I
• Les familles exponentielles statistiques invariantes par les groupes du cône et du paraboloide de révolution
• The Lindsay transform of natural exponential families
• Classical Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution
• Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution (An Introduction)