Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data
ZZ distribution is suitable to describe the life variable of a type of storage products that rarely fail before a given design life，and the proportion of failures has increased significantly after the design life. Based on a progressive type-II censored sample，firstly using Taylor' s formula...
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| Format: | Article |
| Language: | zho |
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Harbin University of Science and Technology Publications
2021-06-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1967 |
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| author | ZHAO Hong-kai ZHANG Guo-zhi WANG Ping |
| author_facet | ZHAO Hong-kai ZHANG Guo-zhi WANG Ping |
| author_sort | ZHAO Hong-kai |
| collection | DOAJ |
| description | ZZ distribution is suitable to describe the life variable of a type of storage products that rarely fail
before a given design life，and the proportion of failures has increased significantly after the design life. Based on a
progressive type-II censored sample，firstly using Taylor' s formula to transform the the nonlinear part of the
likelihood function into a linear expression，the likelihood equation is solvable，and the approximate maximum
likelihood estimation ( AMLE) of the parameter is given. Secondly，using the best linear unbiased estimation
( BLUE) method，a general analytical expression of the parameter is given. At the same time，the expression form
of the estimation is further simplified for two kinds of special progressive type-II censored sample and the required
number table is constructed for the convenience of use. Finally，a numerical comparison of the two methods is
performed，and the results show that the best linear unbiased estimation of ZZ distribution is better than the
approximate maximum likelihood estimation. |
| format | Article |
| id | doaj-art-01b6e03c88664f3097fddae0e4e9203e |
| institution | Kabale University |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2021-06-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-01b6e03c88664f3097fddae0e4e9203e2025-08-20T04:02:17ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832021-06-01260315315910.15938/j.jhust.2021.03.023Parameter Estimation of ZZ Distribution under Progressive Type-II Censored DataZHAO Hong-kai0ZHANG Guo-zhi1WANG Ping2College of Science, Harbin University of Science and Technology, Harbin 150080College of Science, Harbin University of Science and Technology, Harbin 150080College of Science, Harbin University of Science and Technology, Harbin 150080ZZ distribution is suitable to describe the life variable of a type of storage products that rarely fail before a given design life，and the proportion of failures has increased significantly after the design life. Based on a progressive type-II censored sample，firstly using Taylor' s formula to transform the the nonlinear part of the likelihood function into a linear expression，the likelihood equation is solvable，and the approximate maximum likelihood estimation ( AMLE) of the parameter is given. Secondly，using the best linear unbiased estimation ( BLUE) method，a general analytical expression of the parameter is given. At the same time，the expression form of the estimation is further simplified for two kinds of special progressive type-II censored sample and the required number table is constructed for the convenience of use. Finally，a numerical comparison of the two methods is performed，and the results show that the best linear unbiased estimation of ZZ distribution is better than the approximate maximum likelihood estimation.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1967zz distributionmaximum likelihood estimationapproximate maximum likelihood estimationbest linear unbiased estimation |
| spellingShingle | ZHAO Hong-kai ZHANG Guo-zhi WANG Ping Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data Journal of Harbin University of Science and Technology zz distribution maximum likelihood estimation approximate maximum likelihood estimation best linear unbiased estimation |
| title | Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data |
| title_full | Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data |
| title_fullStr | Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data |
| title_full_unstemmed | Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data |
| title_short | Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data |
| title_sort | parameter estimation of zz distribution under progressive type ii censored data |
| topic | zz distribution maximum likelihood estimation approximate maximum likelihood estimation best linear unbiased estimation |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=1967 |
| work_keys_str_mv | AT zhaohongkai parameterestimationofzzdistributionunderprogressivetypeiicensoreddata AT zhangguozhi parameterestimationofzzdistributionunderprogressivetypeiicensoreddata AT wangping parameterestimationofzzdistributionunderprogressivetypeiicensoreddata |