Work

A Duality of the F Distribution

Year: 2026

Type: preprint

Abstract: The F distribution arises naturally in linear regression or analysis of variance. Elementary textbooks state the result in terms of the standard normal random vector and fixed projection matrices. More advanced textbooks and research articles have extended the result to spherically symmetric random vectors. We complement the literature with a dual result that the F distribution arises with a fixed vector and random projection matrices generated by a left-spherical random matrix.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28690

Authors: Zhang, Zifeng, Ding, Peng, Zhou, Wen, Shi, Chenlu

Institutions: Yale University, University of California, Berkeley, New York University, New Jersey Institute of Technology

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223230158

Cites: 3

Cited by:

Related to: 10