Qi, F. Lower Bound of Sectional Curvature of Fisher–Rao Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Results in Mathematics 2021, 76, doi:10.1007/s00025-021-01530-2.
Qi, F. Lower Bound of Sectional Curvature of Fisher–Rao Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Results in Mathematics 2021, 76, doi:10.1007/s00025-021-01530-2.
Qi, F. Lower Bound of Sectional Curvature of Fisher–Rao Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Results in Mathematics 2021, 76, doi:10.1007/s00025-021-01530-2.
Qi, F. Lower Bound of Sectional Curvature of Fisher–Rao Manifold of Beta Distributions and Complete Monotonicity of Functions Involving Polygamma Functions. Results in Mathematics 2021, 76, doi:10.1007/s00025-021-01530-2.
Abstract
In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.
Keywords
necessary and sufficient condition; complete monotonicity; monotonicity; inequality; polygamma function; lower bound; sectional curvature; manifold; beta distribution; convolution theorem for the Laplace transforms and analytic techniques
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
(Click to see Publons profile: )
The commenter has declared there is no conflict of interests.
Comment:
A part of this preprint has been formally published as
Feng Qi, Lower bound of sectional curvature of Fisher--Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions, Results in Mathematics 76 (2021), no. 4, Article 217, 16 pages; available online at https://doi.org/10.1007/s00025-021-01530-2
Commenter:
The commenter has declared there is no conflict of interests.
Feng Qi, Lower bound of sectional curvature of Fisher--Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions, Results in Mathematics 76 (2021), no. 4, Article 217, 16 pages; available online at https://doi.org/10.1007/s00025-021-01530-2