Gamma random variables can be used to simulate chi-square, t, F, beta, and Dirichlet distributions, as well as being useful in their own right. Hence it is important to be able to generate gamma r.v.s as efficiently as possible. we investigate a popular algorithm due to Marsaglia and Tsang, for a 2 1.' (1) If X ~ Gamma(a, 1) then X/X ~ Gamma(a, A). Note that Gamma(a, 8) has the pdf f ( ) = T(a) o-exp (-Bx) . (2) Assume that h(r) is strictly increasing and maps the range of x onto [0, co). If X has density h(x)"-le "()h'(x)/T(a) then Y = h(X) ~ Gamma(a, 1). (3) Given a 2 1 put d= a - 1/3 and c = 1/V9d and then define h : [-1/c, co) - [0, 00) by h(x) = d(1 + cr) . Then, h()"-le "(Oh'(x) o exp(g(x)) where g(x) = dlog((1 + cr) ) - d(1 + cr)* + d and exp(g(x))