The McDonald arcsine distribution: a new model to proportional data

Abstract

We propose a new three-parameter continuous model called the McDonald arcsine distribution, which is a very competitive model to the beta, beta type I and Kumaraswamy distributions for modelling rates and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the density function, moments, generating and quantile functions, mean deviations, two probability measures based on the Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy and cumulative residual entropy. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. An application of the proposed model to real data shows that it can give consistently a better fit than other important statistical models.

• beta distribution
• Kumaraswamy distribution
• maximum-likelihood estimation
• McDonald distribution
• proportional data

We gratefully acknowledge grants from CNPq and FAPESP (Brazil). The authors thank the associate editor for helpful comments which improved the original version of the paper.