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一类新的多元分布及其在蒙特卡洛研究中的应用AI 解读

We consider a new class of multivariate probability distributions having representation X = RLY (p), where R is distributed as √χ 2 (p), L is the Choleski factorization of the scaling matrix Σ, and Y (p) represents an arbitrary distribution on the p-dimensional unit hypersphere. If Y (p) is uniform, then X has a multivariate normal distribution with mean 0 and covariance matrix Σ. The use of classical spherical distributions or other nonuniform distributions for Y (p) leads…

用于非椭圆对称多元数据建模的分布族AI 解读

SUMMARY The paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation. We present a relatively simple family of distributions for use in describing data which are not elliptically symmetric. Properties of the family are discussed and it is shown that multivariate Pareto, Burr and Logistic distributions are special cases. In addition, simulation methods for applications in Monte Carlo robustness studies are…