Exact posterior computation for the binomial–Kumaraswamy model

Abstract

In Bayesian analysis, the well-known beta–binomial model is largely used as a conjugate structure, and the beta prior distribution is a natural choice to model parameters defined in the (0,1) range. The Kumaraswamy distribution has been used as a natural alternative to the beta distribution and has received great attention in statistics in the past few years, mainly due to the simplicity and the great variety of forms it can assume. However, the binomial–Kumaraswamy model is not conjugate, which may limit its use in situations where conjugacy is desired. This work provides the exact posterior distribution for the binomial–Kumaraswamy model using special functions. Besides the exact forms of the posterior moments, the predictive and the cumulative posterior distributions are provided. An example is used to illustrate the theory, in which the exact computation and the MCMC method are compared.