Lower bound of sectional curvature of Fisher-Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions

DOI10.1007/s00025-021-01530-2zbMath1491.44002OpenAlexW4206492238MaRDI QIDQ2242439

Feng Qi

Publication date: 9 November 2021

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-021-01530-2

zbMATH Keywords

monotonicitysectional curvaturelower boundbeta distributionpolygamma functionFisher-Rao metriccomplete monotonicityconvolution theorem for the Laplace transforms

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Probability distributions: general theory (60E05) Gamma, beta and polygamma functions (33B15) Laplace transform (44A10) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) Inequalities involving other types of functions (26D07) Differential geometric aspects of statistical manifolds and information geometry (53B12)

Related Items (8)

A class of completely monotonic functions involving the polygamma functions ⋮ Monotonic properties for ratio of the generalized (p,k)-polygamma functions ⋮ Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function ⋮ Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution ⋮ Complete monotonicity involving the divided difference of polygamma functions ⋮ Integral representations, monotonic properties, and inequalities on extended central binomial coefficient ⋮ Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function ⋮ Decreasing properties of two ratios defined by three and four polygamma functions

Cites Work

• Unnamed Item
• Complete monotonicity of divided differences of the di- and tri-gamma functions with applications
• Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function
• A completely monotonic function involving the tri-gamma function and with degree one
• Some monotonicity properties of gamma and \(q\)-gamma functions
• Necessary and sufficient conditions for functions involving the tri- and tetra-gamma functions to be completely monotonic
• Fisher-Rao geometry of Dirichlet distributions
• Some properties of the divided difference of psi and polygamma functions
• Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
• Some properties of several functions involving polygamma functions and originating from the sectional curvature of the beta manifold
• Quantization and clustering on Riemannian manifolds with an application to air traffic analysis
• Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function
• Necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic
• Complete monotonicity of a family of functions involving the tri- and tetra-gamma functions
• Bernstein functions. Theory and applications

This page was built for publication: Lower bound of sectional curvature of Fisher-Rao manifold of beta distributions and complete monotonicity of functions involving polygamma functions