Inference : a note on estimation in the four-parameter beta distribution

The four-parameter beta distribution is non regular at both lower and upper endpoints in maximum likelihood estimation (MLE). The use of MLE is restricted only in a range of values of the shape parameters. The object of this article is to explore a way of estimating the parameters by placing priors to counteract the shortfalls inherent in the conventional likelihood. The priors are in a general form and therefore the proposed method is generally applicable. The estimators based on the modified likelihood are consistent with optimal rates of convergence.