A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data
With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO<inline-formula><math xmlns="http://www...
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| Format: | Article |
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MDPI AG
2022-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/8/361 |
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| author | Ibrahim Elbatal Sadaf Khan Tassaddaq Hussain Mohammed Elgarhy Naif Alotaibi Hatem E. Semary Mahmoud M. Abdelwahab |
| author_facet | Ibrahim Elbatal Sadaf Khan Tassaddaq Hussain Mohammed Elgarhy Naif Alotaibi Hatem E. Semary Mahmoud M. Abdelwahab |
| author_sort | Ibrahim Elbatal |
| collection | DOAJ |
| description | With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> and leads deliberations, etc., for a specific site or multiple site forms as well as for life testing experiments, we introduced a novel class of distributions known as the Sine Burr <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">X</mi><mo>−</mo><mi mathvariant="script">G</mi></mrow></semantics></math></inline-formula> family. Some exceptional prototypes of this class are proposed. Statistical assets of the presented class, such as density function, complete and incomplete moments, average deviation, and Lorenz and Bonferroni graphs, are proposed. Parameter estimation is made via the likelihood method. Moreover, the application is explained by using four real data sets. We have also illustrated the significance and elasticity of the proposed class in the above-mentioned stochastic phenomenon. |
| first_indexed | 2024-03-09T10:01:17Z |
| format | Article |
| id | doaj.art-38a3c7b1191d47f4a3701fdf02564a34 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T10:01:17Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-38a3c7b1191d47f4a3701fdf02564a342023-12-01T23:24:27ZengMDPI AGAxioms2075-16802022-07-0111836110.3390/axioms11080361A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental DataIbrahim Elbatal0Sadaf Khan1Tassaddaq Hussain2Mohammed Elgarhy3Naif Alotaibi4Hatem E. Semary5Mahmoud M. Abdelwahab6Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, PakistanDepartment of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, PakistanThe Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, EgyptDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi ArabiaWith the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> and leads deliberations, etc., for a specific site or multiple site forms as well as for life testing experiments, we introduced a novel class of distributions known as the Sine Burr <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">X</mi><mo>−</mo><mi mathvariant="script">G</mi></mrow></semantics></math></inline-formula> family. Some exceptional prototypes of this class are proposed. Statistical assets of the presented class, such as density function, complete and incomplete moments, average deviation, and Lorenz and Bonferroni graphs, are proposed. Parameter estimation is made via the likelihood method. Moreover, the application is explained by using four real data sets. We have also illustrated the significance and elasticity of the proposed class in the above-mentioned stochastic phenomenon.https://www.mdpi.com/2075-1680/11/8/361sine <named-content content-type="inline"><inline-formula> <mml:math id="mm2000"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> familyburr <named-content content-type="inline"><inline-formula> <mml:math id="mm2001"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">X</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> familymomentsinference |
| spellingShingle | Ibrahim Elbatal Sadaf Khan Tassaddaq Hussain Mohammed Elgarhy Naif Alotaibi Hatem E. Semary Mahmoud M. Abdelwahab A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data Axioms sine <named-content content-type="inline"><inline-formula> <mml:math id="mm2000"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> family burr <named-content content-type="inline"><inline-formula> <mml:math id="mm2001"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">X</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> family moments inference |
| title | A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data |
| title_full | A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data |
| title_fullStr | A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data |
| title_full_unstemmed | A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data |
| title_short | A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data |
| title_sort | new family of lifetime models theoretical developments with applications in biomedical and environmental data |
| topic | sine <named-content content-type="inline"><inline-formula> <mml:math id="mm2000"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">G</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> family burr <named-content content-type="inline"><inline-formula> <mml:math id="mm2001"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">X</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content> family moments inference |
| url | https://www.mdpi.com/2075-1680/11/8/361 |
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