A new family of multivariate distributions with applications to monte carlo studies

Christopher J. Nachtsheim, Mark E. Johnson

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11 Scopus citations

Abstract

We consider a new class of multivariate probability distributions having representation X = RLY(p), where R is distributed as (Equation presented), 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 to interesting, controllable departures from normality that are particularly relevant to robustness studies. Their use is illustrated in a Monte Carlo investigation of the robustness of Hotelling’s T2. Variate generation routines for the cardioid, triangular, offset normal, wrapped normal, wrapped Cauchy, von Mises, power sine, Fisher, and Bingham distributions are developed.

Original languageEnglish (US)
Pages (from-to)984-989
Number of pages6
JournalJournal of the American Statistical Association
Volume83
Issue number404
DOIs
StatePublished - Dec 1988

Keywords

  • Circular distributions
  • Pearson system
  • Spherical distributions

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