Cumulative Residual Tsallis Entropy-Based Test of Uniformity and Some New Findings

Mohamed S. Mohamed, Haroon M. Barakat, Salem A. Alyami and Mohamed A. Abd Elgawad
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Mohamed S. Mohamed: Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, Egypt
Haroon M. Barakat: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
Salem A. Alyami: Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Mohamed A. Abd Elgawad: Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt

Mathematics, 2022, vol. 10, issue 5, 1-14

Abstract: 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.

Keywords: cumulative residual Tsallis entropy; stability; empirical cumulative distribution function; testing uniformity; Monte Carlo method; test power (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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