A note on the density expansion and generating function of the beta Burr XII

摘要

The five-parameter beta Burr XII (BBXII) was pioneered as an extension of the Burr XII (BXII) distribution. In this work, we obtain a much simpler linear representation for its density to compute its ordinary and incomplete moments, among other related properties. We verify that the BBXI generating function is not convergent for all terms of the series expansion, and then, it is not adequate for all parameter combinations. Therefore, we derive an accurate linear representation for the BBXII density and a new power series for the BXII generating function. We provide Rspienter scripts for these calculations and a numerical study to illustrate the convergence of the density expansion. Many distributions have been proposed in the literature to extend for computing the moments.