Inferência bayesiana para modelos binomiais com priori conjugada baseada em generalizações da distribuição beta

Abstract

The present dissertation aims to propose alternative conjugate prior distributions for the binomial model based on generalizations of the beta distribution. In this context, the developed methodology seeks to estimate the proportion parameter π of the binomial distribution using a Bayesian approach, employing generalizations of the beta distribution as priors in such a way that the posterior distribution also belongs to the same class as the prior. Additionally, the properties of these distributions will be studied in detail, with simulations conducted through random number generation. Their advantages over the beta distribution will be assessed, as the aim is to achieve better fitting results than those obtained by the beta distribution when compared.