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Simulation of some multivariate distributions related to the Dirichlet distribution with application to Monte Carlo simulations

机译:与Dirichlet分布有关的一些多元分布的模拟及其在蒙特卡洛模拟中的应用

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摘要

Simulation of multivariate distributions is important in many applications but remains computationally challenging in practice. In this article, we introduce three classes of multivariate distributions from which simulation can be conducted by means of their stochastic representations related to the Dirichlet random vector. More emphasis is made to simulation from the class of uniform distributions over a polyhedron, which is useful for solving some constrained optimization problems and ha`s many applications in sampling and Monte Carlo simulations. Numerical evidences show that, by utilizing state-of-the-art Dirichlet generation algorithms, the introduced methods become superior to other approaches in terms of computational efficiency.
机译:多元分布的模拟在许多应用中很重要,但实际上在计算上仍然具有挑战性。在本文中,我们介绍了三类多元分布,可以通过它们与Dirichlet随机向量有关的随机表示来进行仿真。多面体上的均匀分布类别更加强调了模拟,这对于解决一些约束优化问题以及在采样和蒙特卡洛模拟中的许多应用非常有用。数值证据表明,通过使用最新的Dirichlet生成算法,在计算效率方面,引入的方法优于其他方法。

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