Correspondance checking software

Question

There's a Gamma distribution $P(A=z)≈\frac{2^{n/2}}{\sqrt{2z\pi}}\exp^{-\frac{z}{2^{1-n}}}$ for $z > 0$ and $0$ otherwise. This distribution has mean $\mu(A) = 2^{-n}$ and standard deviation $\sigma(A)=\sqrt{2}\times2^{-n}$. There're a random variable $v$ and its $K$ observations. I'm looking for a software that will determine if this random variable $v$ matches given distribution by using $K$ observations. First of all, I need the software itself and then mathematical explanation.

Answer 1

You may use the one-sample Kolmogorov-Smirnov test to compare a sample with a reference distribution.

This is implemented in R as ks.test.