TY - JOUR AU - Orsi, Carlo PY - 2022/01/24 Y2 - 2024/03/28 TI - New Developments on the Non-Central Chi-Squared and Beta Distributions JF - Austrian Journal of Statistics JA - AJS VL - 51 IS - 1 SE - Articles DO - 10.17713/ajs.v51i1.1106 UR - https://www.ajs.or.at/index.php/ajs/article/view/1106 SP - 35-51 AB - <p>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.</p> ER -