L moment diagrams for censored observations

Abstract

Observed data sets containing values above or below the analytical threshold of measuring equipment are referred to as censored. Such data are frequently encountered in quality and quantity monitoring applications of water, soil, and air samples. Most of the previous literature on the statistical analysis of censored data relates to the problems of moment, parameter, and quantile estimation methods. Such estimation methods usually assume an underlying probability distribution. Few goodness-of-fit methods exist for censored data. We introduce L moment diagrams for the evaluation of the goodness of fit of alternative distributional hypotheses for left-censored data. Experiments with artificial censored data sets document the conditions under which L moment diagrams should be useful. Our approach, like Hosking's [1995] approach for right censoring, derived L moment diagrams for left-censored observations from partial probability-weighted moments.