BIAS CORRECTION FOR THE SHAPE PARAMETER OF WEIBULL DISTRIBUTION IN GENERALIZED LINEAR MODEL

摘要

It is well known that the estimated shape parameter of Weibull distribution is biased when the Maximum Likelihood Estimation (MLE) method is used. The bias is large enough to cause serious issues when the sample size is small. Many methods have been developed to correct the bias. However, all the current methods are developed for the simple 2 parameter (2-P) Weibull distribution when only the shape parameter beta and the scale parameter eta are in the model. For the generalized linear model (GLM) used in the accelerated life data modeling, the scale parameter eta is a function of one or multiple stresses and this function usually is called life-stress relation. The coefficients for the stresses in the life-stress relation also need to be estimated. Wilh more parameters in the GLM model, the bias of the shape parameter becomes worse. In this paper, a formula that corrects the bias for the Weibull distribution used in the GLM is proposed.