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Improved maximum‐likelihood estimation for the common shape parameter of several Weibull populations

Improved maximum‐likelihood estimation for the common shape parameter of several Weibull populations The biasness problem of the maximum‐likelihood estimate (MLE) of the common shape parameter of several Weibull populations is examined in detail. A modified MLE (MMLE) approach is proposed. In the case of complete and Type II censored data, the bias of the MLE can be substantial. This is noticeable even when the sample size is large. Such a bias increases rapidly as the degree of censorship increases and as more populations are involved. The proposed MMLE, however, is nearly unbiased and much more efficient than the MLE, irrespective of the degree of censorship, the sample sizes, and the number of populations involved. Copyright © 2007 John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

Improved maximum‐likelihood estimation for the common shape parameter of several Weibull populations

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Publisher
Wiley
Copyright
Copyright © 2007 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.678
Publisher site
See Article on Publisher Site

Abstract

The biasness problem of the maximum‐likelihood estimate (MLE) of the common shape parameter of several Weibull populations is examined in detail. A modified MLE (MMLE) approach is proposed. In the case of complete and Type II censored data, the bias of the MLE can be substantial. This is noticeable even when the sample size is large. Such a bias increases rapidly as the degree of censorship increases and as more populations are involved. The proposed MMLE, however, is nearly unbiased and much more efficient than the MLE, irrespective of the degree of censorship, the sample sizes, and the number of populations involved. Copyright © 2007 John Wiley & Sons, Ltd.

Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Sep 1, 2007

References