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If rand() is a function which produces a linearly distributed random number over a range not containing zero, then what type of distribution would rand() / rand() produce?

I know it would center at 1, and there would be a few extreme values very close to zero or very large.

Does this type of random distribution have a name?

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    Suprisingly, [according to Wikipedia](http://en.wikipedia.org/wiki/Ratio_distribution#Uniform_ratio_distribution), the distribution is uniform between 0 and 1 and falls off quadratically after that. It doesn't look like something that would have a name.2012-01-06
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    @Rahul Not really a name, but that is just a convex combination of the uniform $U[0,1]$ distribution and a Pareto distribution (with exponent $\alpha=1$).2012-01-06
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    Sorry, my comment was only considering the special case of a uniform distribution over $(0,1]$.2012-01-06
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    The fact that in the case of $[0,1]$ the density of $Y/X$ is constant on $[0,1]$ is less surprising if you think of it this way: conditioning on any value $X = x \in (0,1]$, the part of the distribution of $Y/X$ on $[0,1]$ is uniform (corresponding to $Y$ in $[0,x]$).2012-01-06
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    @RahulNarain Curiously enough, for a simple model of semiconductor diode in which the current $I$ is related to the applied voltage $V$ as $I=e^V-1$ and $V$ having Laplacian pdf $\frac{1}{2}e^{-|x|}$, the pdf of $I$ is $$f(y) = \begin{cases}\frac{1}{2},& -1 which is just a translated version of the density considered here. And no, it does not have a name among engineers either.2012-01-07

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