Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine
The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/9/1754 |
| _version_ | 1797576562271322112 |
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| author | Neriman Akdam |
| author_facet | Neriman Akdam |
| author_sort | Neriman Akdam |
| collection | DOAJ |
| description | The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals. |
| first_indexed | 2024-03-10T21:54:48Z |
| format | Article |
| id | doaj.art-b4cefcc0c4844bedbabe2846dbe4f704 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:48Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b4cefcc0c4844bedbabe2846dbe4f7042023-11-19T13:12:10ZengMDPI AGSymmetry2073-89942023-09-01159175410.3390/sym15091754Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in MedicineNeriman Akdam0Department of Biostatistics, Faculty of Medicine, Selcuk University, Konya 42131, TurkeyThe aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.https://www.mdpi.com/2073-8994/15/9/1754Rayleigh–Weibull distributionprogressive type-II censored sampleBayes estimatorasymptotic and bootstrap confidence intervalsLindley and Tierney–Kadane approximationMarkov Chain Monte Carlo method |
| spellingShingle | Neriman Akdam Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine Symmetry Rayleigh–Weibull distribution progressive type-II censored sample Bayes estimator asymptotic and bootstrap confidence intervals Lindley and Tierney–Kadane approximation Markov Chain Monte Carlo method |
| title | Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine |
| title_full | Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine |
| title_fullStr | Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine |
| title_full_unstemmed | Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine |
| title_short | Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine |
| title_sort | bayes estimation for the rayleigh weibull distribution based on progressive type ii censored samples for cancer data in medicine |
| topic | Rayleigh–Weibull distribution progressive type-II censored sample Bayes estimator asymptotic and bootstrap confidence intervals Lindley and Tierney–Kadane approximation Markov Chain Monte Carlo method |
| url | https://www.mdpi.com/2073-8994/15/9/1754 |
| work_keys_str_mv | AT nerimanakdam bayesestimationfortherayleighweibulldistributionbasedonprogressivetypeiicensoredsamplesforcancerdatainmedicine |