A characterization of Poisson-Gaussian families by generalized variance

DOI10.3150/bj/1145993979zbMath1106.60014OpenAlexW1976121354MaRDI QIDQ850750

Célestin C. Kokonendji, Afif Masmoudi

Publication date: 6 November 2006

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bj/1145993979

zbMATH Keywords

Laplace transformdeterminantMonge-Ampère equationinfinitely divisible measure\(r\)-reducibilityaffine variance function

Mathematics Subject Classification ID

Probability distributions: general theory (60E05)

Related Items

Multivariate normal \(\alpha\)-stable exponential families ⋮ On the UMVU estimator for the generalized variance of the multinomial family ⋮ A complete characterization of multivariate normal stable Tweedie models through a Monge-Ampère property ⋮ On the Monge-Ampère equation for characterizing gamma-Gaussian model ⋮ Some properties of 2-orthogonal polynomials associated with inverse Gaussian distribution ⋮ Unnamed Item ⋮ Characterization and classification of multiple stable Tweedie models ⋮ Characterization of multinomial exponential families by generalized variance ⋮ Generalized variance functions for infinitely divisible mixture distributions ⋮ On normal stable Tweedie models and power-generalized variance functions of only one component ⋮ A characterization of multivariate normal stable Tweedie models and their associated polynomials

Cites Work

• Unnamed Item
• Unnamed Item
• Natural exponential families with quadratic variance functions
• The diagonal multivariate natural exponential families and their classification
• On the determinant of the second derivative of a Laplace transform
• The \(2d+4\) simple quadratic natural exponential families on \(\mathbb{R}^ d\)
• A property of natural exponential families in \(\mathbb{R}^ n\) with simple quadratic variance functions
• Reference priors for exponential families with simple quadratic variance function
• A Liouville theorem for solutions of the Monge--Ampère equation with periodic data.
• A characterization of Poisson-Gaussian families by convolution-stability
• Generalized variance and exponential families
• On the improper convex affine hyperspheres
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens
• Über die Lösungen der Differentialgleichung \({r t - s^2 = 1}\)
• Estimateurs de la variance généralisée pour des familles exponentielles non gaussiennes
• Complete affine hypersurfaces. Part I. The completeness of affine metrics
• The Monge-Ampère equation