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

2021/07/14 by Carlo Orsi, Orsi, Carlo
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #FOS: Mathematics #Scientific Research and Discoveries #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2107.06689

openalex publication_date 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Moments of the log non-central chi-square distribution
• New insights into non-central beta distributions
• A Novel Approach to Handling the Non-Central Dirichlet Distribution
• On mixture relationships between central and non-central chi-squared difference distributions
• Explicit expressions for moments of the beta Weibull distribution