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Choosing joint distributions so that the variance of the sum is small


  • Knott, Martin
  • Smith, Cyril


The paper considers how to choose the joint distribution of several random variables each with a given marginal distribution so that their sum has a variance as small as possible. A theorem is given that allows the solution of this and of related problems for normal random variables. Several specific applications are given. Additional results are provided for radially symmetric joint distributions of three random variables when the sum is identically zero.

Suggested Citation

  • Knott, Martin & Smith, Cyril, 2006. "Choosing joint distributions so that the variance of the sum is small," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1757-1765, September.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:8:p:1757-1765

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    References listed on IDEAS

    1. Dowson, D. C. & Landau, B. V., 1982. "The Fr├ęchet distance between multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 450-455, September.
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    Cited by:

    1. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    2. Ruodu Wang & Liang Peng & Jingping Yang, 2013. "Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities," Finance and Stochastics, Springer, vol. 17(2), pages 395-417, April.


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