Improved Maximum-Likelihood Estimation for the Common Shape Parameter of Several Weibull Populations

• Main Authors: YANG, Zhenlin, LIN, Dennis K. J.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: bias; mean-squared error; MLE; modified MLE; relative efficiency; shape parameter; type II censored data; Weibull distributions; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/521; https://ink.library.smu.edu.sg/context/soe_research/article/1520/viewcontent/YangLin_ASMBI2007at.pdf
• Institution: Singapore Management University

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.