The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control
In this research work, a new three-parameter lifetime distribution is introduced and studied. It is called the Harris extended Bilal distribution due to its construction from a mixture of the famous Bilal and Harris distributions, resulting from a branching process. The basic properties, such as the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/3/1/13 |
| _version_ | 1797613756883140608 |
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| author | Radhakumari Maya Muhammed Rasheed Irshad Muhammed Ahammed Christophe Chesneau |
| author_facet | Radhakumari Maya Muhammed Rasheed Irshad Muhammed Ahammed Christophe Chesneau |
| author_sort | Radhakumari Maya |
| collection | DOAJ |
| description | In this research work, a new three-parameter lifetime distribution is introduced and studied. It is called the Harris extended Bilal distribution due to its construction from a mixture of the famous Bilal and Harris distributions, resulting from a branching process. The basic properties, such as the moment generating function, moments, quantile function, and Rényi entropy, are discussed. We show that the hazard rate function has ideal features for modeling increasing, upside-down bathtub, and roller-coaster data sets. In a second part, the Harris extended Bilal model is investigated from a statistical viewpoint. The maximum likelihood estimation is used to estimate the parameters, and a simulation study is carried out. The flexibility of the proposed model in a hydrological data analysis scenario is demonstrated using two practical data sets and compared with important competing models. After that, we establish an acceptance sampling plan that takes advantage of all of the features of the Harris extended Bilal model. The operating characteristic values, the minimum sample size that corresponds to the maximum possible defects, and the minimum ratios of lifetime associated with the producer’s risk are discussed. |
| first_indexed | 2024-03-11T06:59:08Z |
| format | Article |
| id | doaj.art-002bbca7e268475dbb5195ae2a53dde7 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-03-11T06:59:08Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-002bbca7e268475dbb5195ae2a53dde72023-11-17T09:20:08ZengMDPI AGAppliedMath2673-99092023-03-013122124210.3390/appliedmath3010013The Harris Extended Bilal Distribution with Applications in Hydrology and Quality ControlRadhakumari Maya0Muhammed Rasheed Irshad1Muhammed Ahammed2Christophe Chesneau3Department of Statistics, University College Thiruvananthapuram, Thiruvananthapuram 695034, IndiaDepartment of Statistics, Cochin University of Science and Technology, Cochin 682022, IndiaDepartment of Statistics, Cochin University of Science and Technology, Cochin 682022, IndiaLaboratoire de Mathématiques Nicolas Oresme (LMNO), Université de Caen-Normandie, 14032 Caen, FranceIn this research work, a new three-parameter lifetime distribution is introduced and studied. It is called the Harris extended Bilal distribution due to its construction from a mixture of the famous Bilal and Harris distributions, resulting from a branching process. The basic properties, such as the moment generating function, moments, quantile function, and Rényi entropy, are discussed. We show that the hazard rate function has ideal features for modeling increasing, upside-down bathtub, and roller-coaster data sets. In a second part, the Harris extended Bilal model is investigated from a statistical viewpoint. The maximum likelihood estimation is used to estimate the parameters, and a simulation study is carried out. The flexibility of the proposed model in a hydrological data analysis scenario is demonstrated using two practical data sets and compared with important competing models. After that, we establish an acceptance sampling plan that takes advantage of all of the features of the Harris extended Bilal model. The operating characteristic values, the minimum sample size that corresponds to the maximum possible defects, and the minimum ratios of lifetime associated with the producer’s risk are discussed.https://www.mdpi.com/2673-9909/3/1/13Harris extended distributionsbilal distributionhazard rate functionquantile functionmaximum likelihood estimationacceptance sampling plans |
| spellingShingle | Radhakumari Maya Muhammed Rasheed Irshad Muhammed Ahammed Christophe Chesneau The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control AppliedMath Harris extended distributions bilal distribution hazard rate function quantile function maximum likelihood estimation acceptance sampling plans |
| title | The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control |
| title_full | The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control |
| title_fullStr | The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control |
| title_full_unstemmed | The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control |
| title_short | The Harris Extended Bilal Distribution with Applications in Hydrology and Quality Control |
| title_sort | harris extended bilal distribution with applications in hydrology and quality control |
| topic | Harris extended distributions bilal distribution hazard rate function quantile function maximum likelihood estimation acceptance sampling plans |
| url | https://www.mdpi.com/2673-9909/3/1/13 |
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