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The computation of bivariate normal and t probabilities, with application to comparisons of three normal means

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  • Kim, Jongphil

Abstract

A novel method for the computation of the bivariate normal and t probability is presented. With suitable transformations, the probability over sets can be easily computed using exact one-dimensional numerical integration. An important application includes computing the exact critical points for the comparisons of three normal means for either the known or unknown variance problem. The critical points by one-dimensional integration can be computed using elementary numerical methods and are more accurate than those by the approximation methods and two-dimensional integration methods. The comparisons of reliability measurements from three populations are presented as an example of a known variance case.

Suggested Citation

  • Kim, Jongphil, 2013. "The computation of bivariate normal and t probabilities, with application to comparisons of three normal means," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 177-186.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:177-186
    DOI: 10.1016/j.csda.2012.08.015
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    References listed on IDEAS

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    1. Hayter, A.J. & Kim, Jongphil & Liu, W., 2008. "Critical point computations for one-sided and two-sided pairwise comparisons of three treatment means," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 463-470, December.
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    Cited by:

    1. Yuge Dong & Qingtong Xie & Shuguang Ding & Liangguo He & Hu Wang, 2022. "The evaluation of bivariate normal probabilities for failure of parallel systems," Statistical Papers, Springer, vol. 63(5), pages 1585-1614, October.

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