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.

## Arguments

- mean
Mean of the random variable.

- sd
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
#>
```