A New Neutrosophic Negative Binomial Distribution: Properties and Applications
Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distributio...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2788265 |
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| author | Rehan Ahmad Khan Sherwani Sadia Iqbal Shumaila Abbas Muhammad Aslam Ali Hussein AL-Marshadi |
| author_facet | Rehan Ahmad Khan Sherwani Sadia Iqbal Shumaila Abbas Muhammad Aslam Ali Hussein AL-Marshadi |
| author_sort | Rehan Ahmad Khan Sherwani |
| collection | DOAJ |
| description | Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including wth, joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously. |
| format | Article |
| id | doaj-art-786f8d40559146fe85be52de4e1e90b6 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-786f8d40559146fe85be52de4e1e90b62025-02-03T01:00:08ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/2788265A New Neutrosophic Negative Binomial Distribution: Properties and ApplicationsRehan Ahmad Khan Sherwani0Sadia Iqbal1Shumaila Abbas2Muhammad Aslam3Ali Hussein AL-Marshadi4College of Statistical and Actuarial SciencesCollege of Statistical and Actuarial SciencesCollege of Statistical and Actuarial SciencesDepartment of StatisticsDepartment of StatisticsMany problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including wth, joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.http://dx.doi.org/10.1155/2021/2788265 |
| spellingShingle | Rehan Ahmad Khan Sherwani Sadia Iqbal Shumaila Abbas Muhammad Aslam Ali Hussein AL-Marshadi A New Neutrosophic Negative Binomial Distribution: Properties and Applications Journal of Mathematics |
| title | A New Neutrosophic Negative Binomial Distribution: Properties and Applications |
| title_full | A New Neutrosophic Negative Binomial Distribution: Properties and Applications |
| title_fullStr | A New Neutrosophic Negative Binomial Distribution: Properties and Applications |
| title_full_unstemmed | A New Neutrosophic Negative Binomial Distribution: Properties and Applications |
| title_short | A New Neutrosophic Negative Binomial Distribution: Properties and Applications |
| title_sort | new neutrosophic negative binomial distribution properties and applications |
| url | http://dx.doi.org/10.1155/2021/2788265 |
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