Question

Suppose X is a gamma variate with E(x) = 3 and var(X ) = .7 Find the parameters 

α and λ of the gamma distribution.

Answer 1

A random variable X which has the gamma distribution with a shape parameter $\alpha$ and a rate parameter $\lambda$ (i.e. $X\sim \Gamma (\alpha ,\lambda )$ ) has the following mean and variance:

$$E(X)=\alpha/\lambda=3$$

$$Var(X)=\alpha/\lambda^2=0.7$$

Hence

$$\alpha=3\lambda$$

$$\dfrac{3\lambda}{\lambda^2}=0.7=>\lambda=\dfrac{30}{7}\approx 4.2857$$

$$\alpha=3\lambda=\dfrac{90}{7}\approx 12.8571$$