Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples
For two families of beta distributions, we show that the generalized Stieltjes transforms of their elements may be written as elementary functions (powers and fractions) of the Stieltjes transform of the Wigner distribution. In particular, we retrieve the examples given by the author in a previous p...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147733 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1477332019-02-16T01:25:13Z Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples Demni, N. For two families of beta distributions, we show that the generalized Stieltjes transforms of their elements may be written as elementary functions (powers and fractions) of the Stieltjes transform of the Wigner distribution. In particular, we retrieve the examples given by the author in a previous paper and relating generalized Stieltjes transforms of special beta distributions to powers of (ordinary) Stieltjes ones. We also provide further examples of similar relations which are motivated by the representation theory of symmetric groups. Remarkably, the power of the Stieltjes transform of the symmetric Bernoulli distribution is a generalized Stietljes transform of a probability distribution if and only if the power is greater than one. As to the free Poisson distribution, it corresponds to the product of two independent Beta distributions in [0,1] while another example of Beta distributions in [−1,1] is found and is related with the Shrinkage process. We close the exposition by considering the generalized Stieltjes transform of a linear functional related with Humbert polynomials and generalizing the symmetric Beta distribution. 2016 Article Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C05; 33C20; 33C45; 44A15; 44A20 DOI:10.3842/SIGMA.2016.035 http://dspace.nbuv.gov.ua/handle/123456789/147733 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
For two families of beta distributions, we show that the generalized Stieltjes transforms of their elements may be written as elementary functions (powers and fractions) of the Stieltjes transform of the Wigner distribution. In particular, we retrieve the examples given by the author in a previous paper and relating generalized Stieltjes transforms of special beta distributions to powers of (ordinary) Stieltjes ones. We also provide further examples of similar relations which are motivated by the representation theory of symmetric groups. Remarkably, the power of the Stieltjes transform of the symmetric Bernoulli distribution is a generalized Stietljes transform of a probability distribution if and only if the power is greater than one. As to the free Poisson distribution, it corresponds to the product of two independent Beta distributions in [0,1] while another example of Beta distributions in [−1,1] is found and is related with the Shrinkage process. We close the exposition by considering the generalized Stieltjes transform of a linear functional related with Humbert polynomials and generalizing the symmetric Beta distribution. |
| format |
Article |
| author |
Demni, N. |
| spellingShingle |
Demni, N. Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Demni, N. |
| author_sort |
Demni, N. |
| title |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples |
| title_short |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples |
| title_full |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples |
| title_fullStr |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples |
| title_full_unstemmed |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples |
| title_sort |
generalized stieltjes transforms of compactly-supported probability distributions: further examples |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147733 |
| citation_txt |
Generalized Stieltjes Transforms of Compactly-Supported Probability Distributions: Further Examples / N. Demni // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 28 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:28:10Z |
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2023-05-20T17:28:10Z |
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1796153363849543680 |