Estimates of some entropies and their relevance in financial market

Abstract

Using various types of bivariate beta priors such as bivariate beta type-I prior, Conner and Mosimann bivariate beta prior and bivariate beta type-III prior, the Bayesian estimate of the entropy of type-(α) and entropy of type-(α,β) are derived for multinomial likelihood. Bayesian estimates of Shannon entropy for different bivariate beta priors can be represented as a limiting function of Bayesian estimates of entropy of type-(α). In this paper, the parameters of the bivariate beta type-III prior under multinomial likelihood in Moody's corporate bond default rates data are selected using the Bayesian estimate of the entropy type -(α).