The Histogram and Boxplot for the Display of Lifetime Data

Abstract

Abstract The importance of histograms and boxplots as exploratory data analysis (EDA) tools has been well established. Yet, adopting them for lifetime data is not straightforward. The first problem, particularly in histograms, is how to deal with censored observations. The second problem is that the underlying distribution of lifetime data is often highly positively skewed. Therefore, in the classical boxplot, large observations can be wrongly diagnosed as outliers. This article extends the definition of the histogram to accommodate for right-censored observations. We apply the “redistribution to the right” method so that the weight of each uncensored observation is actually the jump of the Kaplan—Meier estimation at this point. We also propose modified boxplots to resolve both problems of right censoring and skewness. In our procedure, the fences differ from those of the classical boxplot. Simulation results are presented for an evaluation of our procedure and an example is presented for illustration.