What is a positive, right-tailed random variable that can be set to have mean $0.5$, variance $0.01$?

Question

I am wondering if there exists a right-tailed positive random variable that can be set to have a mean of $0.5$, variance $0.01$. The normal distribution will generate negative values, and it looks impossible to use the Gamma or the Log-Normal for these purposes. Would anyone have any ideas if there exist distributions for which it has a heavy right tail? Thanks.

Answer 1

Here is a density with a power tail:

$$f(x) = \frac{1}{2sx}\exp\left(-\left|\frac{\ln x - m}{s}\right|\right)$$

for the values $m=-0.7116862$ and $s=0.1355204$. The right tail decays like $x^{-8.3789}$, which is not very heavy but still slower than exponential.