Results 211 to 220 of about 212,411 (244)

Haight's distributions as a natural exponential family

Statistics & 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.
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Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits

Neural Information Processing Systems
We prove that single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters. For subgaussian natural exponential families we establish an exact characterization of the growth rate of the self-
Shuai Liu, Alex Ayoub, Flore Sentenac, Xiaoqi Tan, Csaba Szepesv'ari   +4 more
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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 ...
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Conditional natural exponential families

Statistics & Probability Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Natural exponential families of probability distributions and exponential-polynomial approximation

Applied Mathematics and Computation, 1993
A Dirichlet polynomial in a finite linear combination of the functions \(e^{\lambda_ k x}, e^{\lambda_ k x},\dots, x^{m_ k-1} e^{\lambda_ k x}\), \(k=1,2,3,\dots\), where \(\{\lambda_ k\}\) is a sequence of complex numbers and \(\{m_ k\}\) is a sequence of positive integers. The authors [Appl. Math. Comput. 53, No.
Martin, Clyde, Shubov, Victor
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A Classification of Reproducible Natural Exponential Families in the Broad Sense

Journal of Theoretical Probability, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bar-Lev, Shaul K., Casalis, Muriel
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Thompson Sampling-Based Partially Observable Online Change Detection for Exponential Families

INFORMS Journal on Data Science
This paper proposes a holistic sequential change detection framework for partially observable high-dimensional data streams with exponential-family distributions.
Jie Guo, Haodi Yan, Chen Zhang
semanticscholar   +1 more source

Natural Exponential Families and Generalized Hypergeometric Measures

Communications in Statistics - Theory and Methods, 2008
Letbe a positive Borel measure on R n and pFq(a1,... ,ap;b1,... ,bq;s) be a generalized hypergeometric series. We define a generalized hypergeomet- ric measure, µp,q := pFq(a1,... ,ap;b1,... ,bq; ), as a series of convolution powers of the measure , and we investigate classes of probability distri- butions which are expressible as such a measure.
I-Li Lu, Donald St. P. Richards
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On the $q$-continuous natural exponential family

Теория вероятностей и ее применения
В этой статье мы представляем концепцию $q$-натуральных экспоненциальных семейств в рамках $q$-исчисления, которое расширяет классическое понятие, используя $q$-ядро $e_q^{\theta x f(x)^{q-1}}$ вместо традиционного экспоненциального ядра $e^{\theta x}$.
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Inverse Natural Exponential Families on Jr

1994
Abstract Recall that in Chapter 1, Section 1.4 we promised an explanation of the term ‘inverse’ appearing in the inverse Gaussian distribution. We shall now offer an explanation and justification of this usage by introducing the concept of inverse pairs of distributions (measures) and natural exponential families on R The ideas were ...
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