New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme
This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood esti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1713 |
| _version_ | 1797551788841238528 |
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| author | Jung-In Seo Young Eun Jeon Suk-Bok Kang |
| author_facet | Jung-In Seo Young Eun Jeon Suk-Bok Kang |
| author_sort | Jung-In Seo |
| collection | DOAJ |
| description | This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach. |
| first_indexed | 2024-03-10T15:50:57Z |
| format | Article |
| id | doaj.art-ad53fc388fc745928cbb2d07e68554df |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:50:57Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ad53fc388fc745928cbb2d07e68554df2023-11-20T16:05:18ZengMDPI AGMathematics2227-73902020-10-01810171310.3390/math8101713New Approach for a Weibull Distribution under the Progressive Type-II Censoring SchemeJung-In Seo0Young Eun Jeon1Suk-Bok Kang2Division of Convergence Education, Halla University, Wonju-si, Gangwon-do 26404, KoreaDepartment of Statistics, Yeungnam University, Gyeongsan-si, Gyeongsangbuk-do 38541, KoreaDepartment of Statistics, Yeungnam University, Gyeongsan-si, Gyeongsangbuk-do 38541, KoreaThis paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach.https://www.mdpi.com/2227-7390/8/10/1713pivotal quantityprogressive Type-II censored dataWeibull distributionweighted least squares estimation |
| spellingShingle | Jung-In Seo Young Eun Jeon Suk-Bok Kang New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme Mathematics pivotal quantity progressive Type-II censored data Weibull distribution weighted least squares estimation |
| title | New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme |
| title_full | New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme |
| title_fullStr | New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme |
| title_full_unstemmed | New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme |
| title_short | New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme |
| title_sort | new approach for a weibull distribution under the progressive type ii censoring scheme |
| topic | pivotal quantity progressive Type-II censored data Weibull distribution weighted least squares estimation |
| url | https://www.mdpi.com/2227-7390/8/10/1713 |
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