Statistical power of goodness-of-fit tests based on the empirical distribution function for type-I right-censored data

Abstract

In this study, the power of common goodness-of-fit (GoF) statistics based on the empirical distribution function (EDF) was simulated for single type-I right-censored data. The statistical power of the Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics was investigated by varying the null and the alternative distributions, the sample size, the degree of censoring and the significance level. The exponential, Weibull, log-logistic and log-normal lifetime distributions were considered as they are among the most frequently distributions used when modelling censored data. We conclude by giving some general recommendations for testing the distributional assumption of parametric survival models in homogeneous populations when using EDF-based GoF statistics.

Keywords:

• censored data
• goodness-of-fit
• lifetime distributions
• power
• type-I censoring

AMS Subject Classifications:

• 62G10
• 62N99

Acknowledgements

This research was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal – FCT under the project PEst-OE/MAT/UI0006/2011. We are thankful to Professor M. Ivette Gomes for useful advice. Comments during the presentation at LinStat 2010 have been helpful in improving the results presented in this paper.