The Shannon entropy of beta-generated distributions

Beta generated distributions is a broad family of univariate distributions which includes sym- metric as well as skewed models with varying tail weights. It is generated by a transformation of beta random variables by means of a parent distribution. This broad family receives considerable attention in the recent literature (cf. Jones (2004), Zografos and Balakrishnan (2009), among many other). In this paper we discuss about the Shannon entropy of the beta generated distri- butions and more precisely on a specific component of Shannon entropy which depends on the parent model