Results 291 to 300 of about 123,391 (326)

Distribution of Dirichlet l-functions

Lithuanian Mathematical Journal, 1976
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ON DIRICHLET MULTINOMIAL DISTRIBUTIONS

Random Walk, Sequential Analysis and Related Topics, 2006
Dedicated to Professor Y. S. Chow on the Occasion of his 80th Birthday By Robert W. Keener and Wei Biao Wu Abstract Let Y have a symmetric Dirichlet multinomial distributions in R, and let Sm = h(Y1)+· · ·+h(Ym). We derive a central limit theorem for Sm as the sample size n and the number of cells m tend to infinity at the same rate.
ROBERT W. KEENER, WEI BIAO WU
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Generalized Dirichlet distribution in Bayesian analysis

Applied Mathematics and Computation, 1998
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Tzu-Tsung Wong
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Dirichlet Distribution and Orbital Measures

Journal of Lie Theory, 2011
The author considers the probability measure \(M_{n}(k;\alpha)\) on \(\mathbb R\) for \(\alpha\in\mathbb R^{n}\), \(k\in (\mathbb R_{+}^{*})^{n}\) which is related with the Dirichlet distribution \(D_{n}^{(k)}\). The author establishes a Markov-Krein type formula, where \(\alpha=k_{1}+...k_{n}\), which generalizes results given by other authors for ...
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A Characterization of the Dirichlet Distribution

Journal of the American Statistical Association, 1971
Abstract Let X1, X2, ···, Xk be positive random variables such that Σi = 1 k Xi < 1. It is shown, under the assumption of continuous pdf's, that if is independent of the set {Xji j ≠ i} for every i= 1, 2, ···, k then X1, X2, ···, Xk have a Dirichlet distribution, namely αi positive, xi ≥ 0, Σk i = 1 xi < 1.
J. N. Darroch, D. Ratcliff
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Variational learning for Dirichlet process mixtures of Dirichlet distributions and applications

Multimedia Tools and Applications, 2012
In this paper, we propose a Bayesian nonparametric approach for modeling and selection based on a mixture of Dirichlet processes with Dirichlet distributions, which can also be seen as an infinite Dirichlet mixture model. The proposed model uses a stick-breaking representation and is learned by a variational inference method.
Wentao Fan 0001, Nizar Bouguila
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A Dirichlet process mixture of dirichlet distributions for classification and prediction

2008 IEEE Workshop on Machine Learning for Signal Processing, 2008
A significant problem in clustering is the determination of the number of classes which best describes the data. This paper proposes a learning approach based on both Dirichlet process and Dirichlet distribution which provide flexible nonparametric Bayesian framework for non-Gaussian data clustering.
Nizar Bouguila, Djemel Ziou
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The Dirichlet Distribution and Process through Neutralities

Journal of Theoretical Probability, 2007
Some new characterizations are given for the Dirichlet distribution and Dirichlet process in terms of neutrality and neutrality to the right, e.g., Theorem 8: if \((F(t))_{t\in\mathbb R}\) is a stochastic process such that its trajectories are a.s. CDFs, \(( F(t))_{t\in\mathbb R}\) is neutral to the right and \(1-F(t_n)\) is neutral in \((F(t_1), F(t_2)
Bobecka, Konstancja, Wesołowski, Jacek
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On the Inverted Dirichlet Distribution

Communications in Statistics - Theory and Methods, 2009
In this work, we give a representation of the mean expected value of many functionals of inverted Dirichlet distributions in terms of the mean of independent gamma random variables. Some remarkable properties are developed and illustrated. The Gibbs version of the inverted Dirichlet distribution with a selection parameter is considered.
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An inequality for the Dirichlet distribution

Acta Mathematica Hungarica, 1986
The paper proves that the Dirichlet distribution function \[ D(x_ 1,x_ 2,...,x_ n;m_ 1,m_ 2,...,m_ n;m_{n+1})\geq \] \[ \frac{\Gamma (m_ 1+m_ 2+...+m_{n+1})}{\Gamma (m_ 1)\Gamma (m_ 2)...\Gamma (m_{n+1})}B(x_ 1;m_ 1;m_ 2+...+m_{n+1})\times \] \[ B(x_ 2;m_ 2;m_ 3+...+m_{n+1})...B(x_ n;m_ n;m_{n+1}) \] where \(B(x;u;v)=\int^{x}_{0}t^{u-1}(1-t)^{v-1}dt\).
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