Open AccessNew Developments on the Non-Central Chi-Squared and Beta Distributions
Author(s) -
Carlo Orsi
Publication year - 2022
Publication title -
österreichische zeitschrift für statistik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.342
H-Index - 9
ISSN - 1026-597X
DOI - 10.17713/ajs.v51i1.1106
Subject(s) - mathematics , beta distribution , independence (probability theory) , representation (politics) , beta (programming language) , binomial theorem , factorial , negative binomial distribution , moment (physics) , conditional independence , binomial distribution , beta binomial distribution , statistics , combinatorics , mathematical analysis , computer science , poisson distribution , physics , classical mechanics , politics , political science , law , programming language
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.