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 #>