A Mode-based Approach for Lognormal Parameter Estimation on Heavily Censored Data

The density function of the lognormal distribution is unimodal and its mode is always smaller than its median life. For the type-I censoring test, if the censoring time is not larger than the median life, the censoring degree of the dataset obtained in this way will be larger than 50% on average, implying that the dataset is heavily censored. In this case, the classical parameter estimation methods generally cannot provide stable estimates, but a relatively accurate estimate of the mode can be obtained. According to this argument, this paper proposes a mode-based approach for estimating the parameters of the lognormal distribution on heavily censored data. The proposed approach first uses the midpoint Kaplan-Meier estimator to augment the data; then uses the lognormal Q-Q plot to estimate the mode of the density function, from which the scale parameter can be expressed as a function of the shape parameter; and finally uses a single-parameter maximum likelihood method to estimate the shape parameter. Six datasets are analyzed to illustrate the proposed approach and its appropriateness.