Distributional Identities of Beta and Chi-Squared Variates: A Geometrical Interpretation

1992/05/01 by Ralph W. Bailey, R. W. Bailey · 8 citations
Mathematics · #BETA (programming language) #Beta distribution #Bivariate analysis #Combinatorics #Distribution (mathematics) #Extension (predicate logic) #Interpretation (philosophy) #Linguistics #Mathematical analysis #Mathematics #Random variable #Statistical Distribution Estimation and Applications #Statistics #Trigonometry

paper · doi:10.1080/00031305.1992.10475864

published in The American Statistician 46(2), 117-120 (Taylor & Francis)

openalex publication_date 1992/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

A bivariate change of variable is proposed that elucidates the major distributional identities involving the two beta distributions and the chi-squared distribution. These identities are then seen to be the consequence of simple trigonometric relationships. The extension to n dimensions clarifies further identities. There are, however, identities that seem not to fit into this scheme; three of these are reported.

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