The Bayesian estimator of the Shannon entropy is derived using
Connor and Mosimann bivariate beta, bivariate beta type III and bivariate
beta type V distribution distributions. Given the increased focus on the
calculation of regulatory capital held by banks, it is important to have accurate
probability of default estimates. Therefore in this paper the use of the Bayesian
estimator of the Shannon entropy as a measure of certainty, when selecting
the parameters of these various bivariate beta prior distributions in a Bayesian
calibration framework, is illustrated using Moody’s corporate default rates.