A view on weighted exponential entropy and examining some of its features
One of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weight...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2023-11-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_3926_5bf1c736aba9e6decfa9e97e8cd069e1.pdf |
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| author | S. Mazloum Panjehkeh Manije Sanei tabass G. R. Mohtashami Borzadaran Mohammad Amini |
| author_facet | S. Mazloum Panjehkeh Manije Sanei tabass G. R. Mohtashami Borzadaran Mohammad Amini |
| author_sort | S. Mazloum Panjehkeh |
| collection | DOAJ |
| description | One of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weights may reflect some additional characteristics of the events such as their relative importance. In this paper, Axiomatic derivations and properties of weighted exponential entropy parallel to those achieved for weighted entropy are investigated. The relation between weighted exponential entropy of X and a strictly monotone and nonnegative function of X has obtained. The generalized weighted entropy and the generalized weighted exponential entropy for continuous random variable have been presented. |
| first_indexed | 2024-03-07T23:48:13Z |
| format | Article |
| id | doaj.art-880afd1dfcfd4ec49502621bc43e895f |
| institution | Directory Open Access Journal |
| issn | 2251-7952 2645-4505 |
| language | English |
| last_indexed | 2024-03-07T23:48:13Z |
| publishDate | 2023-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj.art-880afd1dfcfd4ec49502621bc43e895f2024-02-19T09:29:20ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052023-11-0113139140210.22103/jmmr.2023.20509.13613926A view on weighted exponential entropy and examining some of its featuresS. Mazloum Panjehkeh0Manije Sanei tabass1G. R. Mohtashami Borzadaran2Mohammad Amini3Department of Statistics, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Statistics, University of Sistan and Baluchestan, Zahedan, IranDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranDepartment of Statistics, Ferdowsi University of Mashhad, Mashhad, IranOne of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weights may reflect some additional characteristics of the events such as their relative importance. In this paper, Axiomatic derivations and properties of weighted exponential entropy parallel to those achieved for weighted entropy are investigated. The relation between weighted exponential entropy of X and a strictly monotone and nonnegative function of X has obtained. The generalized weighted entropy and the generalized weighted exponential entropy for continuous random variable have been presented.https://jmmrc.uk.ac.ir/article_3926_5bf1c736aba9e6decfa9e97e8cd069e1.pdfshannon entropyexponential entropyweighted entropyweighted exponential entropy |
| spellingShingle | S. Mazloum Panjehkeh Manije Sanei tabass G. R. Mohtashami Borzadaran Mohammad Amini A view on weighted exponential entropy and examining some of its features Journal of Mahani Mathematical Research shannon entropy exponential entropy weighted entropy weighted exponential entropy |
| title | A view on weighted exponential entropy and examining some of its features |
| title_full | A view on weighted exponential entropy and examining some of its features |
| title_fullStr | A view on weighted exponential entropy and examining some of its features |
| title_full_unstemmed | A view on weighted exponential entropy and examining some of its features |
| title_short | A view on weighted exponential entropy and examining some of its features |
| title_sort | view on weighted exponential entropy and examining some of its features |
| topic | shannon entropy exponential entropy weighted entropy weighted exponential entropy |
| url | https://jmmrc.uk.ac.ir/article_3926_5bf1c736aba9e6decfa9e97e8cd069e1.pdf |
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