Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings
The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/5/771 |
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| author | Mohamed S. Mohamed Haroon M. Barakat Salem A. Alyami Mohamed A. Abd Elgawad |
| author_facet | Mohamed S. Mohamed Haroon M. Barakat Salem A. Alyami Mohamed A. Abd Elgawad |
| author_sort | Mohamed S. Mohamed |
| collection | DOAJ |
| description | The Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted. |
| first_indexed | 2024-03-09T20:31:11Z |
| format | Article |
| id | doaj.art-84740287a0cc4b018534501b0936ca19 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T20:31:11Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-84740287a0cc4b018534501b0936ca192023-11-23T23:23:24ZengMDPI AGMathematics2227-73902022-02-0110577110.3390/math10050771Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New FindingsMohamed S. Mohamed0Haroon M. Barakat1Salem A. Alyami2Mohamed A. Abd Elgawad3Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, EgyptDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptDepartment of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Benha University, Benha 13518, EgyptThe Tsallis entropy is an extension of the Shannon entropy and is used extensively in physics. The cumulative residual Tsallis entropy, which is a generalization of the Tsallis entropy, plays an important role in the measurement uncertainty of random variables and has simple relationships with other important information and reliability measures. In this paper, some novel properties of the cumulative residual Tsallis entropy are disclosed. Moreover, this entropy measure is applied to testing the uniformity, where the limit distribution and an approximation of the distribution of the test statistic are derived. In addition, the property of stability is discussed. Furthermore, the percentage points and power against seven alternative distributions of this test statistic are presented. Finally, to compare the power of the suggested test with that of other tests of uniformity, a simulation study is conducted.https://www.mdpi.com/2227-7390/10/5/771cumulative residual Tsallis entropystabilityempirical cumulative distribution functiontesting uniformityMonte Carlo methodtest power |
| spellingShingle | Mohamed S. Mohamed Haroon M. Barakat Salem A. Alyami Mohamed A. Abd Elgawad Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings Mathematics cumulative residual Tsallis entropy stability empirical cumulative distribution function testing uniformity Monte Carlo method test power |
| title | Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings |
| title_full | Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings |
| title_fullStr | Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings |
| title_full_unstemmed | Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings |
| title_short | Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings |
| title_sort | cumulative residual tsallis entropy based test of uniformity and some new findings |
| topic | cumulative residual Tsallis entropy stability empirical cumulative distribution function testing uniformity Monte Carlo method test power |
| url | https://www.mdpi.com/2227-7390/10/5/771 |
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