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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| Published in | Statistical theory and related fields Vol. 8; no. 4; pp. 315 - 334 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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01.10.2024
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Domma, Filippo Rehman, Habbiburr Chandra, N. James, A. |
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| Cites_doi | 10.1007/s001840100158 10.1016/j.cam.2020.113316 10.1007/s00362-012-0463-0 10.1016/0047-259X(87)90085-6 10.7712/120217.5399.16870 10.1155/MPE.2005.151 10.1080/03610926.2015.1014110 10.1007/s10260-012-0192-5 10.18576/jsapl/070304 10.1080/10485250701262242 10.1214/13-BA802 10.1080/03610927708827509 10.1007/s001840050030 10.1080/03610918.2016.1169292 10.1142/9789812564511_0001 10.1007/s40745-019-00197-5 10.2307/2336577 10.1080/00949655.2017.1376328 10.33889/IJMEMS.2020.5.1.001 10.2307/2333302 10.1080/01621459.1960.10483368 10.13052/jrss0974-8024.15114 10.1177/0008068317696574 10.1016/j.aej.2021.07.025 10.1080/01621459.1971.10482228 10.1007/s13198-022-01836-6 10.1142/S021853932050014X 10.12988/ams.2017.7398 10.1016/0047-259X(75)90055-X 10.1002/asmb.935 |
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| SubjectTerms | dependence stress–strength Iterated FGM Monte-Carlo simulation Rayleigh distribution reliability |
| Title | Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation |
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