Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation
In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength r...
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Taylor & Francis Group
2024-10-01
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| Series: | Statistical Theory and Related Fields |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/24754269.2024.2398987 |
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| author | N. Chandra A. James Filippo Domma Habbiburr Rehman |
| author_facet | N. Chandra A. James Filippo Domma Habbiburr Rehman |
| author_sort | N. Chandra |
| collection | DOAJ |
| description | In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets. |
| format | Article |
| id | doaj-art-6a47d336df5249ac8d8c8a5b2b8a226c |
| institution | Kabale University |
| issn | 2475-4269 2475-4277 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Taylor & Francis Group |
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| series | Statistical Theory and Related Fields |
| spelling | doaj-art-6a47d336df5249ac8d8c8a5b2b8a226c2024-12-10T16:59:33ZengTaylor & Francis GroupStatistical Theory and Related Fields2475-42692475-42772024-10-018431533410.1080/24754269.2024.2398987Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimationN. Chandra0A. James1Filippo Domma2Habbiburr Rehman3Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry, IndiaDepartment of Statistics and Data Science, CHRIST University, Bengaluru, IndiaDepartment of Economics, Statistics and Finance ‘Giovanni Anania’, University of Calabria, Arcavacata of Rende (CS), ItalyDepartment of Medicine (Biomedical Genetics), Boston University Chobanian & Avedisian School of Medicine, Boston, MA, USAIn this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets.https://www.tandfonline.com/doi/10.1080/24754269.2024.2398987Iterated FGMRayleigh distributiondependence stress–strengthreliabilityMonte-Carlo simulation |
| spellingShingle | N. Chandra A. James Filippo Domma Habbiburr Rehman Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation Statistical Theory and Related Fields Iterated FGM Rayleigh distribution dependence stress–strength reliability Monte-Carlo simulation |
| title | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
| title_full | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
| title_fullStr | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
| title_full_unstemmed | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
| title_short | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
| title_sort | bivariate iterated farlie gumbel morgenstern stress strength reliability model for rayleigh margins properties and estimation |
| topic | Iterated FGM Rayleigh distribution dependence stress–strength reliability Monte-Carlo simulation |
| url | https://www.tandfonline.com/doi/10.1080/24754269.2024.2398987 |
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