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 | 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. |

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.

mom_gamma(mean = 10000, sd = 2000)#> $shape #> [1] 25 #> #> $scale #> [1] 400 #>#> $shape #> [1] 28.44444 25.00000 #> #> $scale #> [1] 281.25 400.00 #>