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Conjugate Exponential Family Priors For Exponential Family Likelihoods
Statistics, 1993General classes of conjugate exponential family priors are identified for exponential family likelihoods. Both joint and conditional specification of the priors are discussed. The normal and inverse Gaussian cases provide illustrations.
Barry C. Arnold +2 more
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Series Statistics, 1979
This paper considers a generalization of the exponential type distributions in the class of exponential families. A characterization and a method of generating an exponential family from a given family are given. In particular the generalized gamma, the generalized Poisson, the inverse Gaussian distributions belonging to this family are discussed.
Jain, G. C., Khan, M. S. H.
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This paper considers a generalization of the exponential type distributions in the class of exponential families. A characterization and a method of generating an exponential family from a given family are given. In particular the generalized gamma, the generalized Poisson, the inverse Gaussian distributions belonging to this family are discussed.
Jain, G. C., Khan, M. S. H.
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Family of Exponentiated Exponential Distribution
2015As was mentioned, in Chap. 1, that Gompertz (1825) raised the extreme value distribution to a positive parameter. Verhulst (1847) introduced the following CDF of a random variable X.
Essam K. AL-Hussaini +1 more
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A note on overdispersed exponential families
Biometrika, 1990Abstract : The issue of creating overdispersion in a given one parameter one dimensional exponential family, by extending it to a two parameter exponential family with the same support, is considered. An easily verifiable sufficient condition for this is derived.
A. E. Gelfand, S. R. Dalal
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Stability for Multivariate Exponential Families
Journal of Mathematical Sciences, 2001Let \(E\) be a Euclidean space, let \(Z :\Omega\to E\) be a nondegenerate random vector, and suppose there is an open convex set \(D\subset E\) such that \(P(Z\in \overline{D}) = 1\). If \(\mu\) is the distribution of \(Z\), define measures \(\mu_\lambda\) by \(d\mu_\lambda(x) = e^{\lambda x}d\mu(x)\), \(x\in E\), for any \(\lambda\) in the dual space \
Balkema, A. A. +2 more
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Atypicality for the class of exponential family
2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016Atypicality is a new concept that uses a codelength-based deviation from the norm to find the interesting rare events. In a previous paper we have developed an information theoretic approach for discrete data. Then in the two other papers, we came up with an extension to the real-valued models for Gaussian and vector Gaussian cases.
Elyas Sabeti, Anders Høst-Madsen
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Information Property of Exponential Families
Theory of Probability & Its Applications, 1986See the review in Zbl 0582.60022.
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HAIRS FOR THE COMPLEX EXPONENTIAL FAMILY
International Journal of Bifurcation and Chaos, 1999In this paper we consider both the dynamical and parameter planes for the complex exponential family Eλ(z)=λez where the parameter λ is complex. We show that there are infinitely many curves or "hairs" in the dynamical plane that contain points whose orbits under Eλ tend to infinity and hence are in the Julia set.
Bodelón, Clara +5 more
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The Exponential Projection Filter and the Selection of the Exponential Family
1996We present the projection filter, an approximate finite-dimensional filter based on the differential geometric approach to statistics. We recall the definition of the projection filter in the case of exponential families, and we give some hints about the selection of the coefficients in the exponential family.
Brigo, Damiano +2 more
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Exponential Families and Game Dynamics
Canadian Journal of Mathematics, 1982A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in
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