On a goodness-of-fit test for normality with unknown parameters and type-II censored data

Abstract

We propose a new goodness-of-fit test for normal and lognormal distributions with unknown parameters and type-II censored data. This test is a generalization of Michael's test for censored samples, which is based on the empirical distribution and a variance stabilizing transformation. We estimate the parameters of the model by using maximum likelihood and Gupta's methods. The quantiles of the distribution of the test statistic under the null hypothesis are obtained through Monte Carlo simulations. The power of the proposed test is estimated and compared to that of the Kolmogorov–Smirnov test also using simulations. The new test is more powerful than the Kolmogorov–Smirnov test in most of the studied cases. Acceptance regions for the PP, QQ and Michael's stabilized probability plots are derived, making it possible to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an illustrative example is presented.

Keywords:

• Kolmogorov–Smirnov test
• maximum likelihood and Gupta's estimators
• Monte Carlo simulation
• PP
• QQ and stabilized probability plots

Acknowledgements

The authors wish to thank the editor and referees for their helpful comments that aided in improving this article. This study was partially supported by PICT 21407 from ANPCYT, X-018 from the Universidad de Buenos Aires and PIP 5505 from CONICET grants, Argentina, and by FONDECYT 1080326 and DIPUV 29-2006 grants, Chile.