Estimators of 2-parameter Weibull distributions from incomplete data with residual lifetimes

It is common for residual lifetimes to be either discarded or treated as if they were right-censored data estimating two-parameter Weibull distributions. The exact maximum likelihood (ML) estimators for dealing with sampled data with residual lifetimes are formulated. Monte Carlo simulation is used to compare the performance of ML estimators for various approaches to the treatment of residual data. Two types of LS (least squares) estimators are also evaluated: LSMR (LS median rank) estimators and LSNPML (LS nonparametric ML) estimators. For ML estimators, the exact method performs better than the approximate ones. Of the two types of LS estimators, the better one is sensitive to the true value of the shape parameter. The exact ML estimation procedure is therefore preferred over the LS procedures even though the former is not always better