The Geometry of Chi-Square Degrees of Freedom

2023/05/17 by James Bernhard, Bernhard, James
Mathematics · Physics and Astronomy · #60E05 (Secondary) #62E10 (Primary) #Advanced Mathematical Theories and Applications #FOS: Computer and information sciences #FOS: Mathematics #Other Statistics (stat.OT) #Probability (math.PR) #Statistical Mechanics and Entropy #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2305.10335

openalex publication_date 2023/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we state and prove a simple geometric interpretation of the degrees of freedom of a chi-square distribution. The general geometric idea goes back at least to Fisher in the 1920s, but the exact result does not appear to have been explicitly stated or proved prior to this paper.

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