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Weighted averages with random proportions that are jointly uniformly distributed over the unit simplex

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  • Soltani, A.R.
  • Homei, H.

Abstract

A weighted Average of n independent continuous random variables X1,...,Xn with random proportions obtained by cutting a simplex by hyper-planes is introduced. A formula between the Stieltjes transforms of the distribution functions of the weighted average and X1,...,Xn is established. The Johnson and Kotz [Johnson, N.L., Kotz, S., 1990. Randomly weighted averages: Some aspects and extensions. Amer. Statist. 44, 245-249] question on the Cauchy distribution characterization of Van Assche [Van Assche, W., 1987. A random variable uniformly distributed between two independent random variables. Sankhya Ser. A 49, 207-211] is answered for n>=2.

Suggested Citation

  • Soltani, A.R. & Homei, H., 2009. "Weighted averages with random proportions that are jointly uniformly distributed over the unit simplex," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1215-1218, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:9:p:1215-1218
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    References listed on IDEAS

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    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    2. Morganna Carmem Diniz & Edmundo de Souza e Silva & H. Richard Gail, 2002. "Calculating the Distribution of a Linear Combination of Uniform Order Statistics," INFORMS Journal on Computing, INFORMS, vol. 14(2), pages 124-131, May.
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    Cited by:

    1. Soltani, A.R., 2022. "Recursive integral equations for random weights averages: Exponential functions and Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 190(C).
    2. Ahmad Soltani & Kamel Abdollahnezhad, 2012. "On adjusted method of moments estimators on uniform distribution samples," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 27-40, April.
    3. Homei, H., 2012. "Randomly weighted averages with beta random proportions," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1515-1520.
    4. Soltani, Ahmad Reza & Roozegar, Rasool, 2012. "On distribution of randomly ordered uniform incremental weighted averages: Divided difference approach," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 1012-1020.

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