Displaying similar documents to “Properties of matrix variate beta type 3 distribution.”

Some Marginal Densities of the Wishart Distribution Някои маргинални плътности на разпределението на Уишарт

Veleva, Evelina (2012)

Union of Bulgarian Mathematicians

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Евелина Илиева Велева - Разпределението на Уишарт се среща в практиката като разпределението на извадъчната ковариационна матрица за наблюдения над многомерно нормално разпределение. Изведени са някои маргинални плътности, получени чрез интегриране на плътността на Уишарт разпределението. Доказани са необходими и достатъчни условия за положителна определеност на една матрица, които дават нужните граници за интегрирането. Wishart distribution arises as the distribution of...

Frames associated with expansive matrix dilations.

Kwok-Pun Ho (2003)

Collectanea Mathematica

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We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.

Wilks' factorization of the complex matrix variate Dirichlet distributions.

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

Revista Matemática Complutense

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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...

Topological degree, Jacobian determinants and relaxation

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2005)

Bollettino dell'Unione Matematica Italiana

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A characterization of the total variation T ⁢ V ⁢ u , Ω of the Jacobian determinant det ⁡ D ⁢ u is obtained for some classes of functions u : Ω → R n outside the traditional regularity space W 1 , n ⁢ Ω ; R n . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity x 0 ∈ Ω . Relations between T ⁢ V ⁢ u , Ω and the distributional determinant Det ⁢ D ⁢ u are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps u ∈ W 1 , p ⁢ Ω ; R n ∩ W 1 , ∞ ⁢ Ω x 0 ; R n . ...