Gamma distribution properties

R defines the Gamma(a,b) with b as a rate (the R helpfile gives the scale version of the Gamma distribution in an equation).  f(x)= b^a/( Gamma(a)) x^(a-1) e^-(bx).  The mean is a/b and the variance a/b^2.

Or Gamma(a, b) parameterized by a mean and variance, where u=a/b and s^2=a/b^2. Then a=u^2/s^2 and b=u/s^2.