Weighted Cumulative Past Extropy and Its Inference
This paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions will be e...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/10/1444 |
| _version_ | 1797473417016901632 |
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| author | Mohammad Reza Kazemi Majid Hashempour Maria Longobardi |
| author_facet | Mohammad Reza Kazemi Majid Hashempour Maria Longobardi |
| author_sort | Mohammad Reza Kazemi |
| collection | DOAJ |
| description | This paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions will be equal. We examine some properties of the WCPJ, and a number of inequalities involving bounds for WCPJ are obtained. Studies related to reliability theory are discussed. Finally, the empirical version of the WCPJ is considered, and a test statistic is proposed. The critical cutoff points of the test statistic are computed numerically. Then, the power of this test is compared to a number of alternative approaches. In some situations, its power is superior to the rest, and in some other settings, it is somewhat weaker than the others. The simulation study shows that the use of this test statistic can be satisfactory with due attention to its simple form and the rich information content behind it. |
| first_indexed | 2024-03-09T20:14:13Z |
| format | Article |
| id | doaj.art-0e087d2917c649309ce75578ceaec159 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T20:14:13Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0e087d2917c649309ce75578ceaec1592023-11-24T00:03:53ZengMDPI AGEntropy1099-43002022-10-012410144410.3390/e24101444Weighted Cumulative Past Extropy and Its InferenceMohammad Reza Kazemi0Majid Hashempour1Maria Longobardi2Department of Statistics, Faculty of Science, Fasa University, Fasa IS74, IranDepartment of Statistics, University of Hormozgan, Bandar Abbas 79177, IranDipartimento di Biologia, Università degli Studi di Napoli Federico II, 80126 Naples, ItalyThis paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions will be equal. We examine some properties of the WCPJ, and a number of inequalities involving bounds for WCPJ are obtained. Studies related to reliability theory are discussed. Finally, the empirical version of the WCPJ is considered, and a test statistic is proposed. The critical cutoff points of the test statistic are computed numerically. Then, the power of this test is compared to a number of alternative approaches. In some situations, its power is superior to the rest, and in some other settings, it is somewhat weaker than the others. The simulation study shows that the use of this test statistic can be satisfactory with due attention to its simple form and the rich information content behind it.https://www.mdpi.com/1099-4300/24/10/1444weighted cumulative past extropyreliability theoryempirical extropygoodness of fit test |
| spellingShingle | Mohammad Reza Kazemi Majid Hashempour Maria Longobardi Weighted Cumulative Past Extropy and Its Inference Entropy weighted cumulative past extropy reliability theory empirical extropy goodness of fit test |
| title | Weighted Cumulative Past Extropy and Its Inference |
| title_full | Weighted Cumulative Past Extropy and Its Inference |
| title_fullStr | Weighted Cumulative Past Extropy and Its Inference |
| title_full_unstemmed | Weighted Cumulative Past Extropy and Its Inference |
| title_short | Weighted Cumulative Past Extropy and Its Inference |
| title_sort | weighted cumulative past extropy and its inference |
| topic | weighted cumulative past extropy reliability theory empirical extropy goodness of fit test |
| url | https://www.mdpi.com/1099-4300/24/10/1444 |
| work_keys_str_mv | AT mohammadrezakazemi weightedcumulativepastextropyanditsinference AT majidhashempour weightedcumulativepastextropyanditsinference AT marialongobardi weightedcumulativepastextropyanditsinference |