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Product of n independent uniform random variables

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  • Dettmann, Carl P.
  • Georgiou, Orestis

Abstract

We give an alternative proof of a useful formula for calculating the probability density function of the product of n uniform, independently and identically distributed random variables. Ishihara (2002) proves the result by induction; here we use Fourier analysis and contour integral methods which provide a more intuitive explanation of how the convolution theorem acts in this case.

Suggested Citation

  • Dettmann, Carl P. & Georgiou, Orestis, 2009. "Product of n independent uniform random variables," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2501-2503, December.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:24:p:2501-2503
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    Cited by:

    1. Benjamin J Finley & Kalevi Kilkki, 2014. "Exploring Empirical Rank-Frequency Distributions Longitudinally through a Simple Stochastic Process," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-14, April.
    2. Amílcar Oliveira & Teresa Oliveira & Antonio Seijas-Macías, 2018. "The uniform distribution product: an approach to the inventory model using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 284-297, January.
    3. Antonio Seijas-Macias & Amílcar Oliveira & Teresa A. Oliveira, 2023. "A New R-Function to Estimate the PDF of the Product of Two Uncorrelated Normal Variables," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    4. Sel Ly & Kim-Hung Pho & Sal Ly & Wing-Keung Wong, 2019. "Determining Distribution for the Product of Random Variables by Using Copulas," Risks, MDPI, vol. 7(1), pages 1-20, February.

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