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The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution

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Abstract

In this paper it is shown how a general two-sided orthant probability for a quadrivariate normal distribution can be evaluated by a one-dimensional numerical integral calculation. The quadrivariate normal distribution can have any covariance matrix and any mean vector. This affords a practical and efficient method for the calculation of these probabilities which is superior to simulation methods. The implementation of the algorithm is discussed, and some examples of its performance are provided.

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Authors and Affiliations

  1. Department of Business Information and Analytics, University of Denver, Denver, CO, USA

    A. J. Hayter

  2. Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China

    Y. Lin

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  1. A. J. Hayter
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  2. Y. Lin
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Correspondence to A. J. Hayter.

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Hayter, A.J., Lin, Y. The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution. Comput Stat 27, 459–471 (2012). https://doi.org/10.1007/s00180-011-0267-z

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  • DOI: https://doi.org/10.1007/s00180-011-0267-z

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