| mom_gamma {hesim} | R Documentation |
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)
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.
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.
Examples
mom_gamma(mean = 10000, sd = 2000)
# The function is vectorized.
mom_gamma(mean = c(8000, 10000), sd = c(1500, 2000))