Just as one can reparameterize the lognormal distribution, which is frequently used in the economic analysis of insurance and, derivatively, insurance regulation, so too with the beta distribution, which is also frequently used. If [latex]\mu[/latex] is the mean of the beta distribution and [latex]\kappa[/latex] is the fraction from 0 to 1 of the maximum possible standard deviation of the beta distribution given its mean, then one can write a modified beta distribution as follows:

Note: corrects sign error in earlier version.