A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine
This study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayl...
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MDPI AG
2025-04-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/4/281 |
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| author | Aadil Ahmad Mir Shamshad Ur Rasool S. P. Ahmad A. A. Bhat Taghreed M. Jawa Neveen Sayed-Ahmed Ahlam H. Tolba |
| author_facet | Aadil Ahmad Mir Shamshad Ur Rasool S. P. Ahmad A. A. Bhat Taghreed M. Jawa Neveen Sayed-Ahmed Ahlam H. Tolba |
| author_sort | Aadil Ahmad Mir |
| collection | DOAJ |
| description | This study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayleigh distribution” (ASPRD), is introduced that features two parameters. We conducted a comprehensive statistical analysis of the ASPRD, exploring its key properties and demonstrating its superior adaptability. The model parameters are estimated using four classical estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spaces estimation (MPSE). Extensive simulation studies confirm these estimation techniques’ robustness, showing that biases, mean squared errors, and root mean squared errors consistently decrease as sample sizes increase. To further validate its applicability, we employ ASPRD on three real-world engineering datasets, showcasing its effectiveness in modeling complex data structures. This work not only strengthens the theoretical framework of probability distributions but also provides valuable tools for practical applications, paving the way for future advancements in statistical modeling. |
| format | Article |
| id | doaj-art-4dd5814c11164ea38e82bda54efa7d40 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-4dd5814c11164ea38e82bda54efa7d402025-08-20T02:24:39ZengMDPI AGAxioms2075-16802025-04-0114428110.3390/axioms14040281A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and MedicineAadil Ahmad Mir0Shamshad Ur Rasool1S. P. Ahmad2A. A. Bhat3Taghreed M. Jawa4Neveen Sayed-Ahmed5Ahlam H. Tolba6Department of Statistics, University of Kashmir, Srinagar 190006, IndiaDepartment of Statistics, University of Kashmir, Srinagar 190006, IndiaDepartment of Statistics, University of Kashmir, Srinagar 190006, IndiaDepartment of Mathematical Sciences, Islamic University of Science and Technology, Pulwama 192122, IndiaDepartment of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics and Statistics, College of Sciences, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThis study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayleigh distribution” (ASPRD), is introduced that features two parameters. We conducted a comprehensive statistical analysis of the ASPRD, exploring its key properties and demonstrating its superior adaptability. The model parameters are estimated using four classical estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spaces estimation (MPSE). Extensive simulation studies confirm these estimation techniques’ robustness, showing that biases, mean squared errors, and root mean squared errors consistently decrease as sample sizes increase. To further validate its applicability, we employ ASPRD on three real-world engineering datasets, showcasing its effectiveness in modeling complex data structures. This work not only strengthens the theoretical framework of probability distributions but also provides valuable tools for practical applications, paving the way for future advancements in statistical modeling.https://www.mdpi.com/2075-1680/14/4/281ASP transformationRayleigh distributionmomentsentropyorder statisticsmaximum likelihood estimation |
| spellingShingle | Aadil Ahmad Mir Shamshad Ur Rasool S. P. Ahmad A. A. Bhat Taghreed M. Jawa Neveen Sayed-Ahmed Ahlam H. Tolba A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine Axioms ASP transformation Rayleigh distribution moments entropy order statistics maximum likelihood estimation |
| title | A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine |
| title_full | A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine |
| title_fullStr | A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine |
| title_full_unstemmed | A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine |
| title_short | A Robust Framework for Probability Distribution Generation: Analyzing Structural Properties and Applications in Engineering and Medicine |
| title_sort | robust framework for probability distribution generation analyzing structural properties and applications in engineering and medicine |
| topic | ASP transformation Rayleigh distribution moments entropy order statistics maximum likelihood estimation |
| url | https://www.mdpi.com/2075-1680/14/4/281 |
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