Results 251 to 260 of about 396,333 (302)

Conjugate Parameterizations for Natural Exponential Families

Journal of the American Statistical Association, 1995
Abstract Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this
Eduardo Gutiérrez-Peña, Adrian F. M. Smith   +1 more
openaire   +2 more sources

Natural exponential families and self-decomposability

Statistics & Probability Letters, 1992
Abstract Let F be a full natural exponential family on R which is generated by a self-decomposable probability distribution P. We provide a necessary and sufficient condition on P under which all other elements of F are also self-decomposable.
Gérard Letac, Daoud Bshouty, Shaul K. Bar-Lev   +2 more
openaire   +2 more sources

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.
V. Seshadri, Célestin C. Kokonendji
openaire   +2 more sources

The diagonal multivariate natural exponential families and their classification [PDF]

Journal of Theoretical Probability, 1994
A natural exponential family (NEF)F in ℝn,n>1, is said to be diagonal if there existn functions,a1,...,an, on some intervals of ℝ, such that the covariance matrixVF(m) ofF has diagonal (a1(m1),...,an(mn)), for allm=(m1,...,mn) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ℝk and ...
Gérard Letac, Daoud Bshouty, Peter Enis, I-Li Lu, Donald St. P. Richards, Shaul K. Bar-Lev   +5 more
openaire   +1 more source

Haight's distributions as a natural exponential family

Statistics & Probability Letters, 1988
Abstract In an index to the distributions of Mathematical Statistics published in 1961, Frank A. Haight considers, without giving any references, the following distribution: α −1 exp (−xe a α −1 ) ∑ n=0 ∞ (n+1) n−1 (n!) 2 x n 1 (0, ∞) (x) d x for 0 for ...
Gérard Letac, V. Seshadri
openaire   +2 more sources

A note on natural exponential families with cuts

Statistics & Probability Letters, 2003
Abstract Let μ be a positive measure defined on the product of two vector spaces E = E 1 × E 2 . Let F = F ( μ ) be a natural exponential family (NEF) generated by μ such that the projection of F on E 1 constitutes a NEF on E 1 . This property, called a cut on E 1 , has been defined and characterized by Barndorff-Nielsen (Information
Shaul K. Bar-Lev, Denys Pommeret
openaire   +2 more sources

Conditional natural exponential families

Statistics & Probability Letters, 2006
Abstract Let F = { P θ ; θ ∈ Θ } be a natural exponential family on R d and let H be an exposed face of the closed convex hull of the F support. The aim of this paper is to study the asymptotic behavior of the law P θ + λ u as λ increases to + ∞ , for all u exterior normal vector of H.
openaire   +2 more sources

Natural Exponential Families and Umbral Calculus

1998
We use the Umbral Calculus to investigate the relation between natural exponential families and Sheffer polynomials. As a corollary, we obtain a new transparent proof of Feinsilver’s theorem which says that natural exponential families have a quadratic variance function if and only if their associated Sheffer polynomials are orthogonal.
A. Di Bucchianico, D.E. Loeb
openaire   +3 more sources

Predictive Fit for Natural Exponential Families

Biometrika, 1989
SUMMARY The paper examines predictive distributions, concentrating on measuring their fit to the true distribution by average Kullback-Leibler divergence. The notion of an 'averaged bootstrap' predictive distribution is introduced. This predictive distribution is shown to be asymptotically superior to the estimative distribution, in terms of average ...
openaire   +2 more sources

Natural exponential families of probability distributions and exponential-polynomial approximation

Applied Mathematics and Computation, 1993
Abstract We consider expansions of regular functions in series with respect to infinite systems of Dirichlet polynomials, i.e., combinations of polynomials and exponents. We show that for every natural exponential family of probability measures on a real line and an infinite sequence of complex numbers, whose real parts belong to the natural ...
Clyde F. Martin, V. I. Shubov
openaire   +2 more sources