A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data
In statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025172 |
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| author | Alanazi Talal Abdulrahman Khudhayr A. Rashedi Tariq S. Alshammari Eslam Hussam Amirah Saeed Alharthi Ramlah H Albayyat |
| author_facet | Alanazi Talal Abdulrahman Khudhayr A. Rashedi Tariq S. Alshammari Eslam Hussam Amirah Saeed Alharthi Ramlah H Albayyat |
| author_sort | Alanazi Talal Abdulrahman |
| collection | DOAJ |
| description | In statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution can fit symmetric, complex, heavy-tailed, and asymmetric data sets. Several key mathematical and statistical results were investigated, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis for the suggested model. In addition, various estimation strategies, including maximum likelihood estimation and Bayes estimation, were used to estimate the model parameters. The Metropolis-Hastings technique was used for Bayesian estimates under the square error loss function. A comprehensive simulation study was used to evaluate the performance of the derived estimators. The model's flexibility was tested on two data sets from the industrial domain, revealing that it offers greater flexibility compared to existing distributions. |
| format | Article |
| id | doaj-art-2e914b8b3a6247cca8ef0c5ddd189dc0 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2e914b8b3a6247cca8ef0c5ddd189dc02025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011023710373310.3934/math.2025172A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial dataAlanazi Talal Abdulrahman0Khudhayr A. Rashedi1Tariq S. Alshammari2Eslam Hussam3Amirah Saeed Alharthi4Ramlah H Albayyat5Department of Mathematics, College of Science University of Ha'il, Hail, Saudi ArabiaDepartment of Mathematics, College of Science University of Ha'il, Hail, Saudi ArabiaDepartment of Mathematics, College of Science University of Ha'il, Hail, Saudi ArabiaDepartment of Accounting, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, P.O. Box 11099, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi ArabiaIn statistical modeling, generating a novel family of distributions is essential to develop new and adaptable models to analyze various data sets. This paper presents a new asymmetric extension of the Rayleigh distribution called the generalized Kumaraswamy Rayleigh model. The proposed distribution can fit symmetric, complex, heavy-tailed, and asymmetric data sets. Several key mathematical and statistical results were investigated, including moments, moment-generating functions, variance, dispersion index, skewness, and kurtosis for the suggested model. In addition, various estimation strategies, including maximum likelihood estimation and Bayes estimation, were used to estimate the model parameters. The Metropolis-Hastings technique was used for Bayesian estimates under the square error loss function. A comprehensive simulation study was used to evaluate the performance of the derived estimators. The model's flexibility was tested on two data sets from the industrial domain, revealing that it offers greater flexibility compared to existing distributions.https://www.aimspress.com/article/doi/10.3934/math.2025172bayesian estimatorheavy-tailedindustrial domainmetropolis-hastings techniquesimulation experimentssquare error loss function |
| spellingShingle | Alanazi Talal Abdulrahman Khudhayr A. Rashedi Tariq S. Alshammari Eslam Hussam Amirah Saeed Alharthi Ramlah H Albayyat A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data AIMS Mathematics bayesian estimator heavy-tailed industrial domain metropolis-hastings technique simulation experiments square error loss function |
| title | A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data |
| title_full | A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data |
| title_fullStr | A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data |
| title_full_unstemmed | A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data |
| title_short | A new extension of the Rayleigh distribution: Methodology, classical, and Bayes estimation, with application to industrial data |
| title_sort | new extension of the rayleigh distribution methodology classical and bayes estimation with application to industrial data |
| topic | bayesian estimator heavy-tailed industrial domain metropolis-hastings technique simulation experiments square error loss function |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025172 |
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