Compute the shape and scale (or rate) parameters of the gamma distribution using method of moments for the random variable of interest.
mom_gamma(mean, sd, scale = TRUE)Mean of the random variable.
Standard deviation of the random variable.
Logical. If TRUE (default), then the scale parameter is returned; otherwise, the rate parameter is returned.
If scale = TRUE, then a list containing the parameters shape and scale; otherwise,
if scale = FALSE, then a list containing the parameters shape and rate.
If \(\mu\) is the mean and
\(\sigma\) is the standard deviation of the random variable, then the method
of moments estimates of the parameters shape = \(\alpha > 0\) and
scale = \(\theta > 0\) are:
$$\theta = \frac{\sigma^2}{\mu}$$
and
$$\alpha = \frac{\mu}{\theta}$$
The inverse of the scale parameter, \(\beta = 1/\theta\), is the rate parameter.