On some goodness-of-fit tests and their connection to graphical methods with uncensored and censored data

Abstract

In this work, we present goodness-of-fit tests related to the Kolmogorov-Smirnov and Michael statistics and connect them to graphical methods with uncensored and censored data. The Anderson-Darling test is often empirically more powerful than the Kolmogorov-Smirnov test. However, the former one cannot be related to graphical tools by means of probability plots, as the Kolmogorov-Smirnov test does. The Michael test is, in some cases, more powerful than the Anderson-Darling and Kolmogorov-Smirnov tests and can also be related to probability plots. We consider the Kolmogorov-Smirnov and Michael tests for detecting whether any distribution is suitable or not to model censored or uncensored data. We conduct numerical studies to show the performance of these tests and the corresponding graphical tools. Some comments related to big data and lifetime analysis, under the context of this study, are provided in the conclusions of this work.