Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions
In this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and originating from the estimation of the sectional curvatur...
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/1/44 |
| _version_ | 1797358464510459904 |
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| author | Feng Qi Ravi Prakash Agarwal |
| author_facet | Feng Qi Ravi Prakash Agarwal |
| author_sort | Feng Qi |
| collection | DOAJ |
| description | In this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and originating from the estimation of the sectional curvature of the Fisher–Rao geometry of the Dirichlet distributions in the two-dimensional case. |
| first_indexed | 2024-03-08T15:02:25Z |
| format | Article |
| id | doaj.art-6bdb80f4b7374521947c9ab4f7b7f390 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T15:02:25Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6bdb80f4b7374521947c9ab4f7b7f3902024-01-10T15:03:24ZengMDPI AGMathematics2227-73902023-12-011214410.3390/math12010044Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma FunctionsFeng Qi0Ravi Prakash Agarwal1School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, ChinaDepartment of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USAIn this paper, the authors review and survey some results published since 2020 about (complete) monotonicity, inequalities, and their necessary and sufficient conditions for several newly introduced functions involving polygamma functions and originating from the estimation of the sectional curvature of the Fisher–Rao geometry of the Dirichlet distributions in the two-dimensional case.https://www.mdpi.com/2227-7390/12/1/44sectional curvaturepolygamma functioninequalitycomplete monotonicitynecessary and sufficient conditionlower bound |
| spellingShingle | Feng Qi Ravi Prakash Agarwal Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions Mathematics sectional curvature polygamma function inequality complete monotonicity necessary and sufficient condition lower bound |
| title | Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions |
| title_full | Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions |
| title_fullStr | Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions |
| title_full_unstemmed | Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions |
| title_short | Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions |
| title_sort | several functions originating from fisher rao geometry of dirichlet distributions and involving polygamma functions |
| topic | sectional curvature polygamma function inequality complete monotonicity necessary and sufficient condition lower bound |
| url | https://www.mdpi.com/2227-7390/12/1/44 |
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