Product of \(n\) independent uniform random variables. (English) Zbl 1176.62007
Summary: 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. T. Ishihara [Trans. Jap. Soc. Indust. Appl. Math. 12, No. 3, 197ff (Japanese) (2002)] proved 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.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 60E05 | Probability distributions: general theory |
| 65C60 | Computational problems in statistics (MSC2010) |
| 65T60 | Numerical methods for wavelets |
| 65D30 | Numerical integration |
References:
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