alpha and beta using mean and variance of beta distribution
It is well known that for beta(alpha, beta), the mean is alpha/(alpha+beta) and the variance is (alpha*beta)/((alpha+beta)^2*(alpha+beta+1)). https://en.wikipedia.org/wiki/Beta_distribution Then it is easy to reverse the model to estimate alpha and beta when mean and variance are known: alpha/p = alpha+beta beta = alpha/p - alpha = alpha * (1/p -1) v = (alpha*(alpha/p - alpha)) / ((alpha + alpha/p - alpha)^2 * (alpha + alpha/p - alpha +1)) v = (alpha*(alpha * (1/p -1))) / ((alpha + alpha/p - alpha)^2 * (alpha + alpha/p - alpha +1)) v = (alpha^2 * (1/p -1)) / ((alpha^2 (1/p^2)) * (alpha/p + 1)) v = (alpha * (1/p -1)) / ((alpha (1/p^2)) * (alpha/p + 1)) v = (1/p -1) / (((1/p^2)) * (alpha/p + 1)) 1/v = ((1/p^2) * (alpha/p + 1)) / (1/p -1) (1/p -1) / v = (1/p^2) * (alpha/p + 1) (1/p -1) / ( v * (1/p^2) ) = alpha/p + 1 (1/p -1) / ( v * (1/p^2) ) - 1 = alpha/p p * ((1/p -1) / ( v * (1/p^2) ) - 1) = alpha Let try: alpha = 1 beta = 1 (p <- alpha/(alpha+beta))