mom_gamma: Method of moments for gamma distribution
Description
Compute the shape and scale (or rate) parameters of the gamma distribution
using method of moments for the random variable of interest.
Usage
mom_gamma(mean, sd, scale = TRUE)
Value
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.
Arguments
mean
Mean of the random variable.
sd
Standard deviation of the random variable.
scale
Logical. If TRUE (default), then the scale parameter is returned; otherwise,
the rate parameter is returned.
Details
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.