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Randomly weighted averages with beta random proportions

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  • Homei, H.

Abstract

A weighted average of two independent continuous random variables X1 and X2 with random proportions obtained by Beta distribution is introduced. A formula between the Stieltjes transforms of the distribution functions of the weighted averages and X1, X2 is established. We show that, among some other distributions, the Cauchy distribution and the power semicircle distribution can be characterized in a particular way by means of this construction.

Suggested Citation

  • Homei, H., 2012. "Randomly weighted averages with beta random proportions," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1515-1520.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1515-1520
    DOI: 10.1016/j.spl.2012.04.017
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hazhir Homei, 2015. "A novel extension of randomly weighted averages," Statistical Papers, Springer, vol. 56(4), pages 933-946, November.

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