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.Comment: accepted for publication at Austrian Journal of Statistics on 06 May
202