Method of moments for beta distribution

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
#>