New Developments on the Non-Central Chi-Squared and Beta Distributions
Abstract
New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending factorial of a binomial are the main ingredients of the first approach, whereas the second one hinges on an interesting relationship of conditional independence and a simple conditional density of the latter model. Then, a simulation study is carried out in order to pursue a twofold purpose: providing numerical validations of the derived moment formulas on one side and discussing the advantages of the new formulas over the existing ones on the other.
Cite
@article{arxiv.2107.06689,
title = {New Developments on the Non-Central Chi-Squared and Beta Distributions},
author = {Carlo Orsi},
journal= {arXiv preprint arXiv:2107.06689},
year = {2021}
}
Comments
accepted for publication at Austrian Journal of Statistics on 06 May 2021