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)`

## 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.

## 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`

.

## 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.

## Examples

```
mom_gamma(mean = 10000, sd = 2000)
#> $shape
#> [1] 25
#>
#> $scale
#> [1] 400
#>
# The function is vectorized.
mom_gamma(mean = c(8000, 10000), sd = c(1500, 2000))
#> $shape
#> [1] 28.44444 25.00000
#>
#> $scale
#> [1] 281.25 400.00
#>
```