Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring
The present paper has developed the preliminary test estimators (PTEs) of the model parameter raised to certain power, σp, and the two measures of reliability, namely, the reliability function, R(t ) and the reliability of an item or a system, P of an exponentiated distribution, under Type- II censo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Bologna
2019-07-01
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| Series: | Statistica |
| Subjects: | |
| Online Access: | https://rivista-statistica.unibo.it/article/view/8543 |
| _version_ | 1819089638224035840 |
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| author | Ajit Chaturvedi Anshika Bhatnagar |
| author_facet | Ajit Chaturvedi Anshika Bhatnagar |
| author_sort | Ajit Chaturvedi |
| collection | DOAJ |
| description | The present paper has developed the preliminary test estimators (PTEs) of the model parameter raised to certain power, σp, and the two measures of reliability, namely, the reliability function, R(t ) and the reliability of an item or a system, P of an exponentiated distribution, under Type- II censoring, based on their uniformly minimum variance unbiased estimators (UMVUEs) and maximum likelihood estimators (MLEs). The preliminary test confidence intervals (PTCIs) are also developed for σ, R(t ) and P based on their UMVUEs and MLEs. Further, the paper has derived expression for coverage probability of the PTCI of the model parameter, σ. Merits of the proposed PTEs are also established through analysis of simulated numerical data. |
| first_indexed | 2024-12-21T22:11:07Z |
| format | Article |
| id | doaj.art-dd6cfba9d56d42a5a9297f9a2fc4348b |
| institution | Directory Open Access Journal |
| issn | 0390-590X 1973-2201 |
| language | English |
| last_indexed | 2024-12-21T22:11:07Z |
| publishDate | 2019-07-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Statistica |
| spelling | doaj.art-dd6cfba9d56d42a5a9297f9a2fc4348b2022-12-21T18:48:36ZengUniversity of BolognaStatistica0390-590X1973-22012019-07-0179111112910.6092/issn.1973-2201/85438232Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II CensoringAjit Chaturvedi0Anshika Bhatnagar1University of DelhiUniversity of DelhiThe present paper has developed the preliminary test estimators (PTEs) of the model parameter raised to certain power, σp, and the two measures of reliability, namely, the reliability function, R(t ) and the reliability of an item or a system, P of an exponentiated distribution, under Type- II censoring, based on their uniformly minimum variance unbiased estimators (UMVUEs) and maximum likelihood estimators (MLEs). The preliminary test confidence intervals (PTCIs) are also developed for σ, R(t ) and P based on their UMVUEs and MLEs. Further, the paper has derived expression for coverage probability of the PTCI of the model parameter, σ. Merits of the proposed PTEs are also established through analysis of simulated numerical data.https://rivista-statistica.unibo.it/article/view/8543exponentiated distributionspreliminary test estimatortype-ii censoringuniformly minimum variance unbiased estimatormaximum likelihood estimator |
| spellingShingle | Ajit Chaturvedi Anshika Bhatnagar Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring Statistica exponentiated distributions preliminary test estimator type-ii censoring uniformly minimum variance unbiased estimator maximum likelihood estimator |
| title | Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring |
| title_full | Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring |
| title_fullStr | Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring |
| title_full_unstemmed | Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring |
| title_short | Establishment of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of an Exponentiated Distribution Based on Type-II Censoring |
| title_sort | establishment of preliminary test estimators and preliminary test confidence intervals for measures of reliability of an exponentiated distribution based on type ii censoring |
| topic | exponentiated distributions preliminary test estimator type-ii censoring uniformly minimum variance unbiased estimator maximum likelihood estimator |
| url | https://rivista-statistica.unibo.it/article/view/8543 |
| work_keys_str_mv | AT ajitchaturvedi establishmentofpreliminarytestestimatorsandpreliminarytestconfidenceintervalsformeasuresofreliabilityofanexponentiateddistributionbasedontypeiicensoring AT anshikabhatnagar establishmentofpreliminarytestestimatorsandpreliminarytestconfidenceintervalsformeasuresofreliabilityofanexponentiateddistributionbasedontypeiicensoring |