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.
Usage
mom_beta(mean, sd)
Value
A list containing the parameters shape1 and shape2.
Arguments
mean
Mean of the random variable.
sd
Standard deviation of the random variable.
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
$$\beta = (1 - \mu) \left(\frac{\mu(1-\mu)}{\sigma^2}-1 \right)$$