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PreprintCC BY 4.0arXiv

Convexity of a ratio function involving polygamma functions and monotonicity of the sectional curvature of the Fisher--Rao manifold

  • Feng Qi
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Abstract

This paper proves that the sectional curvature of the Fisher--Rao manifold of beta distributions, restricted to the diagonal, is strictly decreasing. The proof is based on a general convexity lemma for ratios involving positive decreasing functions and is applied to a quotient of polygamma functions.

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Cite

BibTeXRIS
BibTeX
@misc{qi2026convexity,
  title = {{Convexity of a ratio function involving polygamma functions and monotonicity of the sectional curvature of the Fisher--Rao manifold}},
  author = {Feng Qi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.10628},
  eprint = {2609.10628},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10628},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Convexity of a ratio function involving polygamma functions and monotonicity of the sectional curvature of the Fisher--Rao manifold
AU  - Feng Qi
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.10628
UR  - https://arxiv.org/abs/2609.10628
AB  - This paper proves that the sectional curvature of the Fisher--Rao manifold of beta distributions, restricted to the diagonal, is strictly decreasing. The proof is based on a general convexity lemma for ratios involving positive decreasing functions and is applied to a quotient of polygamma functions.
ER  -