Compute the parameters shape1 and shape2 of the beta distribution using method of moments given the mean and standard deviation of the random variable of interest.

mom_beta(mean, sd)

## Arguments

mean Mean of the random variable. Standard deviation of the random variable.

## Value

A list containing the parameters shape1 and shape2.

## 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 shape1 = $$\alpha > 0$$ and shape2 = $$\beta > 0$$ are: $$\alpha = \mu \left(\frac{\mu(1-\mu)}{\sigma^2}-1 \right)$$ and $$\beta = (1 - \mu) \left(\frac{\mu(1-\mu)}{\sigma^2}-1 \right)$$

## Examples

mom_beta(mean = .8, sd = .1)
#> $shape1 #> [1] 12 #> #>$shape2
#> [1] 3
#> # The function is vectorized.
mom_beta(mean = c(.6, .8), sd = c(.08, .1))
#> $shape1 #> [1] 21.9 12.0 #> #>$shape2
#> [1] 14.6  3.0
#>