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A conditional characterization of the multivariate normal distribution

Author

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  • Arnold, Barry C.
  • Castillo, Enrique
  • Sarabia, Jose María

Abstract

If X is a k-dimensional random vector, we denote by X(i,j) the vector X with coordinates i and j deleted. If for each i, j the conditional distribution of Xi, Xj given X(i,j) = x(i,j) is classical bivariate normal for each then it is shown that X has a classical k-variate normal distribution.

Suggested Citation

  • Arnold, Barry C. & Castillo, Enrique & Sarabia, Jose María, 1994. "A conditional characterization of the multivariate normal distribution," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 313-315, March.
    • Handle: RePEc:eee:stapro:v:19:y:1994:i:4:p:313-315
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    Cited by:

    1. Bischoff, Wolfgang, 1996. "Characterizing multivariate normal distributions by some of its conditionals," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 105-111, February.

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