Estimation of Moments and Quantiles using Censored Data

Censored data sets are often encountered in water quality investigations and streamflow analyses. A Monte Carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets. These techniques include a lognormal maximum likelihood estimator (MLE), a log-probability plot regression estimator, and a new log-partial probability-weighted moment estimator. Data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables. A “robust” fill-in method, which circumvents transformation bias in the real space moments, was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation. Regardless of the underlying distribution, the MLE generally performed as well as or better than the other estimators, though the moment and quantile estimators using all three techniques had comparable log-space root mean square errors (rmse) for censoring at or below the 20th percentile for samples sizes of n=10, the 40th percentile for n=25, and the 60th percentile for n=50. Comparison of the log-space rmse and real-space rmse indicated that a log-space rmse was a better overall metric of estimator precision.