On the Moments of the Beta Normal Distribution

Abstract

Eugene et al. [Eugene, N., Lee, C., Famoye, F. (2002). Beta-normal distribution and its applications. Commun. Stat. Theory Meth. 31:497–512] introduced the beta normal distribution, generated from the logit of a beta random variable. The only properties of the distribution studied by them are its first moments for some particular values of the parameters. In this article, we derive a more general expression for the nth moment of the beta normal distribution. We also consider several particular cases (including those cases considered by Eugene et al.). Apart from being more general, the proof of our results are simpler and avoid the differential equations approach taken by Eugene et al.

Key Words:

• Beta distribution
• Error function
• Normal distribution

Acknowledgments

The authors would like to thank the referee for carefully reading the paper and for his/her help in improving the paper.