Multivariate Distributions, Overview†

Multivariate distributions arise throughout statistics and applied probability and they are defined on finite-dimensional spaces. They serve as probabilistic models for dependent outcomes of random experiments. Biometric data typically comprises observations on multiple characteristics for each experimental subject, and joint distributions are central to the modeling and analyses of such data. From multivariate distributions, the distributions of various sample statistics of note in statistical inference can be derived. Multivariate distributions also characterize the behavior of stochastic processes through properties of their finite-dimensional projections. Keywords: correlation; regression; convergence; dispersion matrix; covariance matrix; multivariate Bartlett test; stochastic ordering; Wishart distribution; Dirichlet distribution; Weibull distribution; hypergeometric distributions

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