Maximum likelihood estimation under misspecified lognormal and Weibull distributions

This article provides expressions for computing the asymptotic distribution of maximum likelihood estimators of lognormal and Weibull parameters when the distribution is misspecified and data are Type I or II censored. The results can be used to derive the asymptotic normal distribution of observed bias in estimation of functions of model parameters such as quantiles. The methods are applied to a Type I censored dataset on locomotive controls. The results are used to derive test plans that are bias-robust for estimating quantiles. Values of the proportions failing that minimize asymptotic mean square error and absolute asymptotic bias are tabulated.