A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods
In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies ar...
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oai:doaj.org-article:5bcc77acdb4448ed84941bd3b020abe72021-11-08T02:36:39ZA New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods1875-919X10.1155/2021/2404997https://doaj.org/article/5bcc77acdb4448ed84941bd3b020abe72021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2404997https://doaj.org/toc/1875-919XIn this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates.Abdullah M. AlmarashiAli AlgarniAmal S. HassanM. ElgarhyFarrukh JamalChristophe ChesneauKhudir AlrashidiWali Khan MashwaniHeba F. NagyHindawi LimitedarticleComputer softwareQA76.75-76.765ENScientific Programming, Vol 2021 (2021) |
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Computer software QA76.75-76.765 |
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Computer software QA76.75-76.765 Abdullah M. Almarashi Ali Algarni Amal S. Hassan M. Elgarhy Farrukh Jamal Christophe Chesneau Khudir Alrashidi Wali Khan Mashwani Heba F. Nagy A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| description |
In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates. |
| format |
article |
| author |
Abdullah M. Almarashi Ali Algarni Amal S. Hassan M. Elgarhy Farrukh Jamal Christophe Chesneau Khudir Alrashidi Wali Khan Mashwani Heba F. Nagy |
| author_facet |
Abdullah M. Almarashi Ali Algarni Amal S. Hassan M. Elgarhy Farrukh Jamal Christophe Chesneau Khudir Alrashidi Wali Khan Mashwani Heba F. Nagy |
| author_sort |
Abdullah M. Almarashi |
| title |
A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| title_short |
A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| title_full |
A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| title_fullStr |
A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| title_full_unstemmed |
A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods |
| title_sort |
new estimation study of the stress-strength reliability for the topp–leone distribution using advanced sampling methods |
| publisher |
Hindawi Limited |
| publishDate |
2021 |
| url |
https://doaj.org/article/5bcc77acdb4448ed84941bd3b020abe7 |
| work_keys_str_mv |
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