estimate Gamma parameters based on mean and variance

Question

I am following these two approaches (which are the same)this and this, to estimate the two parameters of Gamma dist based on mean and var. I am not sure why I cannot get the same mean and var from rgamma based on the estimated parameters in R:

 mean1=20
 var1=30

 shapeg = (mean1*2)/var1
 scaleg = var1/mean1

 nn=(rgamma(1000, shape = shapeg, scale = scaleg))
 mean(nn);
 var(nn);

 > mean(nn);
 [1] 1.975715
 > var(nn);
 [1] 3.6593

Based on https://stat.ethz.ch/R-manual/R-devel/library/stats/html/GammaDist.html

The Gamma distribution with parameters shape = a and scale = s

The mean and variance are E(X) = as and Var(X) = as^2.

Based on this: https://stats.stackexchange.com/questions/280459/estimating-gamma-distribution-parameters-using-sample-mean-and-std

$\mbox{Var}[X] = \alpha \theta^2$

therefore, $\theta$ must be equal to scale in R. SO I am replacing the parameters correctly.

Answer 1

I think the mistake is in your code. It looks like you tried to square with *2 instead of ^2. Maybe you were thinking of Python, which would use **2.