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A note on the sum of uniform random variables


  • Buonocore, Aniello
  • Pirozzi, Enrica
  • Caputo, Luigia


An inductive procedure is used to obtain distributions and probability densities for the sum Sn of independent, non-equally uniform random variables. Some known results are then shown to follow immediately as special cases. Under the assumption of equally uniform random variables some new formulas are obtained for probabilities and means related to Sn. Finally, some new recursive formulas involving distributions are derived.

Suggested Citation

  • Buonocore, Aniello & Pirozzi, Enrica & Caputo, Luigia, 2009. "A note on the sum of uniform random variables," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2092-2097, October.
  • Handle: RePEc:eee:stapro:v:79:y:2009:i:19:p:2092-2097

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    References listed on IDEAS

    1. S. Sadooghi-Alvandi & A. Nematollahi & R. Habibi, 2009. "On the distribution of the sum of independent uniform random variables," Statistical Papers, Springer, vol. 50(1), pages 171-175, January.
    2. Heinrich Potuschak & Werner Müller, 2009. "More on the distribution of the sum of uniform random variables," Statistical Papers, Springer, vol. 50(1), pages 177-183, January.
    3. David Bradley & Ramesh Gupta, 2002. "On the Distribution of the Sum of n Non-Identically Distributed Uniform Random Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 689-700, September.
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    Cited by:

    1. Mohammed W. Baidas & Emad Alsusa & Motasem Alfarra & Mubarak Al-Mubarak, 2020. "Multi-relay selection in energy-harvesting cooperative wireless networks: game-theoretic modeling and analysis," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 73(2), pages 289-311, February.
    2. Fragkiskos Bersimis & Demosthenes Panagiotakos & Malvina Vamvakari, 2017. "Investigating the sensitivity function's monotony of a health-related index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1680-1706, July.

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