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Sum of squares of uniform random variables

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  • Weissman, Ishay

Abstract

Given a set of n independent uniform random variables on [0,1], this paper deals with the distribution of their sum of squares. Explicit solutions are given for n=2,3 and 4. Graphical presentations are given for n up to 12. The case n=2 is special in the sense that the density function is constant on [0,1], a property noticed first by Adi Ben-Israel.

Suggested Citation

  • Weissman, Ishay, 2017. "Sum of squares of uniform random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 147-154.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:147-154
    DOI: 10.1016/j.spl.2017.05.018
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    Cited by:

    1. Alhakim, Abbas & Molchanov, S., 2019. "The density flatness phenomenon," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 156-161.
    2. Forrester, Peter J., 2018. "Comment on “Sum of squares of uniform random variables” by I. Weissman," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 118-122.
    3. Weissman, Ishay, 2023. "Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 194(C).

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    Keywords

    Convolution; Geometric approach;

    Statistics

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