Uniform Distributions Ratio Let $\xi$ is $U(0, 1)$, $\nu$ is $U(0, 1)$. What type of distribution is $g = \frac{\xi}{\nu}$? I have build logarithm of $g$, here is the plot but it seems like it is not normal distribution:
Distribution Hist
 A: Assming independence...
Consider the following system
$$\begin{cases}
g=\frac{\xi}{\nu} \\
u=\xi
\end{cases}$$
The Jacobian is $|J|=\frac{\xi}{g^2}$
thus your density is
$$f_G(g)=\frac{1}{2}\cdot\mathbb{1}_{[0;1)}(g)+\frac{1}{2g^2}\cdot\mathbb{1}_{[1;+\infty)}(g)$$
A: Since $\log 1/\nu$ and $\log 1/\xi$ are exponentially distributed, your plot, $\log g$, follows the Difference Between Exponential Distributions.
A: 
How did you receive the last statement? –

after calculating the jacobian that is $|J|=\frac{u}{g^2}$ you conclude that the joint density is
$$f(u,g)=\frac{u}{g^2}$$
but in the system you see that
$$0<\nu=\frac{u}{g}<1$$
Now, when $0<g<1$ this means that $0<u<g$ thus in this interval to get $f(g)$ you have to integrate the joint density in
$$f(g)=\int_0^g \frac{u}{g^2}du=\frac{1}{2}$$
When $g>1$ there are no problem for $\frac{u}{g}$ to be less than one thus you integrate
$$f(g)=\int_0^1 \frac{u}{g^2}du=\frac{1}{2g^2}$$
... put all together and get the result
this is the drawing of your density

