A Duality of the F Distribution

@misc{zhang2026duality,
  title = {{A Duality of the F Distribution}},
  author = {Zifeng Zhang and Peng Ding and Wen Zhou and Chenlu Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28690},
  eprint = {2610.28690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28690},
}

TY  - UNPB
TI  - A Duality of the F Distribution
AU  - Zifeng Zhang
AU  - Peng Ding
AU  - Wen Zhou
AU  - Chenlu Shi
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28690
UR  - https://arxiv.org/abs/2610.28690
AB  - 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.
ER  -