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Probability Integrals of the Multivariate t Distribution

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  • Saralees Nadarajah
  • Samuel Kotz

Abstract

Results on probability integrals of multivariate t distributions are reviewed. The results discussed include: Dunnett and Sobel's probability integrals, Gupta and Sobel's probability integrals, John's probability integrals, Amos and Bulgren's probability integrals, Steffens' non‐central probabilities, Dutt's probability integrals, Amos' probability integral, Fujikoshi's probability integrals, probabilities of cone, probabilities of convex polyhedra, probabilities of linear inequalities, maximum probability content, and Monte Carlo evaluation. On examine les résultats d'intégrales de probabilité de distributions multivariées t. Les résultats discutés incluent: intégrales de probabilité de Dunnett et Sobel, intégrales de probabilité de Gupta et Sobel, intégrales de probabilité de John, intégrales de probabilité de Amos et Bulgren, probabilités non centrées de Steffen, intégrales de probabilité de Dutt, intégrale de probabilité de Amos, intégrales de probabilité de Fujikoshi, probabilités de cônes, probabilités de polyèdres convexes, probabilités d'inégalités linéaires, probabilité maximale, évaluation de Monte Carlo.

Suggested Citation

  • Saralees Nadarajah & Samuel Kotz, 2008. "Probability Integrals of the Multivariate t Distribution," International Statistical Review, International Statistical Institute, vol. 76(1), pages 58-88, April.
    • Handle: RePEc:bla:istatr:v:76:y:2008:i:1:p:58-88
    DOI: 10.1111/j.1751-5823.2007.00021.x
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