| Summary: | 碩士 === 國立政治大學 === 統計研究所 === 101 === Dirichlet distributions can be taken as a high-dimensioned version of beta distributions, and it has many applications, such as conjugate prior distribution in bayesian Inference and construction of the model of multivariate data. When the parameters of Dirichlet distributions are α_1=⋯=α_(n+1)=1, it can be regarded as uniform distribution within a n-dimensioned simplex. High-dimensioned uniform distribution in irregular domains has various applications, such as species surveys in quadrats sampling and Monte Carlo simulation, which often need to generate uniform random vectors over polyhedrons. With Dirichlet distributions, it is more efficient to generate uniform random vectors in irregular domain. This article evaluated the module in R, “rBeta2009” [8], originally designed by Cheng et al. (2012), and discusses how to generate other multivariate distributions by using the Dirichlet algorithm in the package, including generation of (i) Inverted Dirichlet random vectors (ii) Liouville random vectors, and (iii) uniform random vectors over polyhedrons with linear constraints. The article also verified that the method is more efficient than the older package in R. (by comparing the CPU time.)
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