Bounds for Shannon and Zipf‐Mandelbrot entropies
Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies....
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| Autor*in: |
Adil Khan, Muhammad [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: Copyright © 2017 John Wiley & Sons, Ltd. |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Mathematical methods in the applied sciences - Chichester, West Sussex : Wiley, 1979, 40(2017), 18, Seite 7316-7322 |
|---|---|
| Übergeordnetes Werk: |
volume:40 ; year:2017 ; number:18 ; pages:7316-7322 |
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| DOI / URN: |
10.1002/mma.4531 |
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| 520 | |a Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. | ||
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10.1002/mma.4531 doi PQ20171228 (DE-627)OLC199917545X (DE-599)GBVOLC199917545X (PRQ)p661-40ab6c0c5d528b03722d95f5941cee9a3fce8376289b6f2fc61f0437b490ce93 (KEY)0093427520170000040001807316boundsforshannonandzipfmandelbrotentropies DE-627 ger DE-627 rakwb eng 510 DE-600 31.80 bkl Adil Khan, Muhammad verfasserin aut Bounds for Shannon and Zipf‐Mandelbrot entropies 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. Nutzungsrecht: Copyright © 2017 John Wiley & Sons, Ltd. Zipf‐Mandelbrot entropy Shannon entropy Jensen inequality convex function Entropy (Information theory) Information theory Entropy Pečaric, Đilda oth Pečarić, Josip oth Enthalten in Mathematical methods in the applied sciences Chichester, West Sussex : Wiley, 1979 40(2017), 18, Seite 7316-7322 (DE-627)130619051 (DE-600)795328-8 (DE-576)016125967 0170-4214 nnns volume:40 year:2017 number:18 pages:7316-7322 http://dx.doi.org/10.1002/mma.4531 Volltext http://onlinelibrary.wiley.com/doi/10.1002/mma.4531/abstract https://search.proquest.com/docview/1968883466 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4318 31.80 AVZ AR 40 2017 18 7316-7322 |
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10.1002/mma.4531 doi PQ20171228 (DE-627)OLC199917545X (DE-599)GBVOLC199917545X (PRQ)p661-40ab6c0c5d528b03722d95f5941cee9a3fce8376289b6f2fc61f0437b490ce93 (KEY)0093427520170000040001807316boundsforshannonandzipfmandelbrotentropies DE-627 ger DE-627 rakwb eng 510 DE-600 31.80 bkl Adil Khan, Muhammad verfasserin aut Bounds for Shannon and Zipf‐Mandelbrot entropies 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. Nutzungsrecht: Copyright © 2017 John Wiley & Sons, Ltd. Zipf‐Mandelbrot entropy Shannon entropy Jensen inequality convex function Entropy (Information theory) Information theory Entropy Pečaric, Đilda oth Pečarić, Josip oth Enthalten in Mathematical methods in the applied sciences Chichester, West Sussex : Wiley, 1979 40(2017), 18, Seite 7316-7322 (DE-627)130619051 (DE-600)795328-8 (DE-576)016125967 0170-4214 nnns volume:40 year:2017 number:18 pages:7316-7322 http://dx.doi.org/10.1002/mma.4531 Volltext http://onlinelibrary.wiley.com/doi/10.1002/mma.4531/abstract https://search.proquest.com/docview/1968883466 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4318 31.80 AVZ AR 40 2017 18 7316-7322 |
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10.1002/mma.4531 doi PQ20171228 (DE-627)OLC199917545X (DE-599)GBVOLC199917545X (PRQ)p661-40ab6c0c5d528b03722d95f5941cee9a3fce8376289b6f2fc61f0437b490ce93 (KEY)0093427520170000040001807316boundsforshannonandzipfmandelbrotentropies DE-627 ger DE-627 rakwb eng 510 DE-600 31.80 bkl Adil Khan, Muhammad verfasserin aut Bounds for Shannon and Zipf‐Mandelbrot entropies 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. Nutzungsrecht: Copyright © 2017 John Wiley & Sons, Ltd. Zipf‐Mandelbrot entropy Shannon entropy Jensen inequality convex function Entropy (Information theory) Information theory Entropy Pečaric, Đilda oth Pečarić, Josip oth Enthalten in Mathematical methods in the applied sciences Chichester, West Sussex : Wiley, 1979 40(2017), 18, Seite 7316-7322 (DE-627)130619051 (DE-600)795328-8 (DE-576)016125967 0170-4214 nnns volume:40 year:2017 number:18 pages:7316-7322 http://dx.doi.org/10.1002/mma.4531 Volltext http://onlinelibrary.wiley.com/doi/10.1002/mma.4531/abstract https://search.proquest.com/docview/1968883466 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4318 31.80 AVZ AR 40 2017 18 7316-7322 |
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Adil Khan, Muhammad |
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bounds for shannon and zipf‐mandelbrot entropies |
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Bounds for Shannon and Zipf‐Mandelbrot entropies |
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Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. |
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Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. |
| abstract_unstemmed |
Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy. |
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Bounds for Shannon and Zipf‐Mandelbrot entropies |
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http://dx.doi.org/10.1002/mma.4531 http://onlinelibrary.wiley.com/doi/10.1002/mma.4531/abstract https://search.proquest.com/docview/1968883466 |
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Pečaric, Đilda Pečarić, Josip |
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