Beta-Normal Distribution: Bimodality Properties and Application

Abstract

The beta-normal distribution is characterized by four parameters that jointly describe the location, the scale and the shape properties. The beta-normal distribution can be unimodal or bimodal. This paper studies the bimodality properties of the beta-normal distribution. The region of bimodality in the parameter space is obtained. The beta-normal distribution is applied to fit a numerical bimodal data set. The beta-normal fits are compared with the fits of mixture-normal distribution through simulation.