Results 201 to 210 of about 54,704 (250)

Haight's distributions as a natural exponential family

Statistics and Probability Letters, 1988
In an index to the distributions of mathematical statistics, \textit{F. A. Haight} [J. Res. Nat. Bureau of Standards 65B(1), 23-60 (1961)] considers, without giving any references, the following distribution: \[ \alpha^{-1}\exp (-xe^{\alpha}\alpha^{- 1})\sum^{\infty}_{n=0}(n+1)^{n-1}(n!)^{-2}x^ n\mathbf{1}_{(0,\infty)}(x)dx\quad for\quad ...
Letac, Gérard, Seshadri, V.
exaly   +2 more sources

Natural exponential families and self-decomposability

Statistics and Probability Letters, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gérard Letac, Daoud Bshouty, Shaul K Bar-Lev   +2 more
exaly   +2 more sources

Parameterizations for Natural Exponential Families with Quadratic Variance Functions

Journal of the American Statistical Association, 1994
Abstract 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.
Elizabeth H Slate
exaly   +4 more sources

Cuts in Natural Exponential Families

Theory of Probability & Its Applications, 1996
The concept of cuts [\textit{O. E. Barndorff-Nielsen}, Exponential families and conditioning. Sc. D. Thesis, Univ. Copenhagen (1973; Zbl 0297.62001)], which is intimately connected to the concepts of \(S\)-ancillarity and \(S\)-sufficiency, has been studied in the context of general exponential families.
Barndorff-Nielsen, O. E., Koudou, A. E.
openaire   +3 more sources

A note on natural exponential families with cuts

Statistics & Probability Letters, 2003
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Bar-Lev, Shaul K., Pommeret, Denys
openaire   +2 more sources

Laplace Approximations for Natural Exponential Families with Cuts

Scandinavian Journal of Statistics, 1998
Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter ...
Efstathiou, M., Gutiérrez-Peña, E., Smith, A. F. M.   +2 more
openaire   +2 more sources

New q-general natural exponential family

Communications in Statistics Part B: Simulation and Computation
Nahla Ben Salah
exaly   +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.
Di Bucchianico, A., Loeb, D.E.
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.
Kokonendji, C. C., Seshadri, V.
openaire   +1 more source

The Reconstruction of Natural Exponential Families by Their Marginals

Journal of Mathematical Sciences, 2001
Two-dimensional natural exponential families of distributions with cumulant function \(k(\theta_1,\theta_2)\) are considered. It is shown that the following relations hold \[ \begin{aligned} k(\theta_1,\theta_2) &= k_1(\theta_1+\beta_1(\theta_2))+k_2(\theta_2)- k_1(\theta_1^0+\beta_1(\theta_2))\\ &= k_2(\theta_2+\beta_2(\theta_1))+k_1(\theta_1)- k_1 ...
openaire   +2 more sources