A simple formula based on quantiles for the moments of beta generalized distributions

Abstract

In this article, we derive explicit expansions for the moments of beta generalized distributions from power series expansions for the quantile functions of the baseline distributions. We apply our formula to the beta normal, beta Student t, beta gamma and beta beta generalized distributions. We propose a simple way to express the quantile function of any beta generalized distribution as a power series expansion with known coefficients.

Keywords:

• beta beta distribution
• beta gamma distribution
• beta normal distribution
• beta Student t distribution
• quantile function

Acknowledgements

The author thanks CNPq for providing financial support. The author also thanks the referee and the editor for carefully reading the article and for their help in improving it.

Notes

http://functions.wolfram.com/06.23.06.0004.01.