A family of shrinkage estimators for Weibull shape parameter in censored sampling |
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Authors: | Housila Prasad Singh Sharad Saxena Harshada Joshi |
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Affiliation: | (1) School of Studies in Statistics, Vikram University, Ujjain, 456 010, MP, India;(2) Institute of Management, Nirma University, S-G Highway, Ahmedabad, 382 481, India |
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Abstract: | In this paper a new class of shrinkage estimators has been introduced for the shape parameter in an independently identically distributed two-parameterWeibull model under censored sampling. The main idea is to incorporate the prior guessed value by correcting the standard estimator, which is essentially an unbiased estimator, with optimally weighted ratios of the guessed value and the standard estimator, instead of considering a convex combination of the standard estimator and the difference of the guessed value and the standard estimator. The resulting estimator dominates the standard estimator in a surprisingly large neighborhood of the guessed value. The suggested estimator has also been compared with the minimum mean squared error estimator and a class of estimators suggested by Singh and Shukla in IAPQR Trans 25(2), 107–118, 2000. It is found that the suggested class of estimators has lesser bias as well as lesser mean squared error than its competitors subject to certain conditions. |
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Keywords: | Weibull distribution Shape parameter Guessed value Progressive type II censoring Bias Mean squared error Percent relative efficiency |
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