WIAS Preprint No. 2005, (2014)

Computing and approximating multivariate chi-square probabilities


  • Stange, Jens
  • Loginova, Nina
  • Dickhaus, Thorsten

2010 Mathematics Subject Classification

  • 60E05 60E15 62E17 65D20


  • Bonferroni inequalities, chain factorization, correlation matrix, effective number of tests, linkage disequilibrium, m-factorial matrix, product-type probability approximations, sub-Markovian, Wishart matrix


We consider computational methods for evaluating and approximating multivariate chi-square probabilities in cases where the pertaining correlation matrix or blocks thereof have a low-factorial representation. To this end, techniques from matrix factorization and probability theory are applied. We outline a variety of statistical applications of multivariate chi-square distributions and provide a system of MATLAB programs implementing the proposed algorithms. Computer simulations demonstrate the accuracy and the computational efficiency of our methods in comparison with Monte Carlo approximations, and a real data example from statistical genetics illustrates their usage in practice.

Appeared in

  • J. Statist. Comput. Simul., 86:6 (2016), pp. 1233--1247.

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