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Improved maximum‐likelihood estimation for the common shape parameter of several Weibull populations
Author(s) -
Yang Zhenlin,
Lin Dennis K. J.
Publication year - 2007
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.678
Subject(s) - weibull distribution , statistics , maximum likelihood , sample (material) , sample size determination , censorship , mathematics , econometrics , estimation , degree (music) , estimation theory , economics , physics , law , management , political science , thermodynamics , acoustics
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.