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New Developments on the Non-Central Chi-Squared and Beta Distributions


  • Carlo Orsi


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.


How to Cite

Orsi, C. New Developments on the Non-Central Chi-Squared and Beta Distributions. Austrian Journal of Statistics, 51(1), 35–51. Retrieved from