Product of n independent uniform random variables

CP Dettmann; O Georgiou

doi:10.1016/j.spl.2009.09.004

Product of n independent uniform random variables

CP Dettmann
, O Georgiou

Research output: Contribution to journal › Article (Academic Journal) › peer-review

29 Citations (Scopus)

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.

Translated title of the contribution	Product of n independent uniform random variables
Original language	English
Pages (from-to)	2501 - 2503
Number of pages	3
Journal	Statistics and Probability Letters
Volume	79, issue 24
DOIs	https://doi.org/10.1016/j.spl.2009.09.004
Publication status	Published - Dec 2008

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Publisher: Elsevier

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10.1016/j.spl.2009.09.004

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title = "Product of n independent uniform random variables",

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.",

author = "CP Dettmann and O Georgiou",

note = "Publisher: Elsevier",

year = "2008",

month = dec,

doi = "10.1016/j.spl.2009.09.004",

language = "English",

volume = "79, issue 24",

pages = "2501 -- 2503",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Product of n independent uniform random variables

AU - Dettmann, CP

AU - Georgiou, O

N1 - Publisher: Elsevier

PY - 2008/12

Y1 - 2008/12

N2 - 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.

AB - 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.

U2 - 10.1016/j.spl.2009.09.004

DO - 10.1016/j.spl.2009.09.004

M3 - Article (Academic Journal)

SN - 0167-7152

VL - 79, issue 24

SP - 2501

EP - 2503

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Product of n independent uniform random variables

Abstract

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