Expansions for the multivariate chi-square distribution

T. Royen

Journal of Multivariate Analysis, 1991, vol. 38, issue 2, 213-232

Abstract: Three classes of expansions for the distribution function of the [chi]k2(d, R)-distribution are given, where k denotes the dimension, d the degree of freedom, and R the "accompanying correlation matrix." The first class generalizes the orthogonal series with generalized Laguerre polynomials, originally given by Krishnamoorthy and Parthasarathy [12]. The second class contains always absolutely convergent representations of the distribution function by univariate chi-square distributions and the third class provides also the probabilities for any unbounded rectangular regions. In particular, simple formulas are given for the three-variate case including singular correlation matrices R, which simplify the computation of third order Bonferroni inequalities, e.g., for the tail probabilities of max{[chi]i21 3).

Keywords: multivariate; chi-square; distribution; multivariate; gamma; distribution; multivariate; Rayleigh; distribution (search for similar items in EconPapers)
Date: 1991
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Citations: View citations in EconPapers (7)

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