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Weighted halfspace depth

Daniel Hlubinka, Lukáš Kotík, Ondřej Vencálek (2010)

Kybernetika

Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

Let α be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α . I give an elementary proof of the necessary and sufficient condition for α to be a locally finite complex measure (= complex Radon measure).

Why Jordan algebras are natural in statistics: quadratic regression implies Wishart distributions

G. Letac, J. Wesołowski (2011)

Bulletin de la Société Mathématique de France

If the space 𝒬 of quadratic forms in n is splitted in a direct sum 𝒬 1 ... 𝒬 k and if X and Y are independent random variables of n , assume that there exist a real number a such that E ( X | X + Y ) = a ( X + Y ) and real distinct numbers b 1 , . . . , b k such that E ( q ( X ) | X + Y ) = b i q ( X + Y ) for any q in 𝒬 i . We prove that this happens only when k = 2 , when n can be structured in a Euclidean Jordan algebra and when X and Y have Wishart distributions corresponding to this structure.

Wilks' factorization of the complex matrix variate Dirichlet distributions.

Xinping Cui, Arjun K. Gupta, Daya K. Nagar (2005)

Revista Matemática Complutense

In this paper, it has been shown that the complex matrix variate Dirichlet type I density factors into the complex matrix variate beta type I densities. Similar result has also been derived for the complex matrix variate Dirichlet type II density. Also, by using certain matrix transformations, the complex matrix variate Dirichlet distributions have been generated from the complex matrix beta distributions. Further, several results on the product of complex Wishart and complex beta matrices with...

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