Shannon entropy as a measure of certainty in a Bayesian calibration framework with bivariate beta priors

Abstract

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.