A New Goodness-of-Fit Test for Censored Data with an Application in Monitoring Processes

Abstract

In this article, we propose a new goodness-of-fit test for Type I or Type II censored samples from a completely specified distribution. This test is a generalization of Michael's test for censored data, which is based on the empirical distribution and a variance stabilizing transformation. Using Monte Carlo methods, the distributions of the test statistics are analyzed under the null hypothesis. Tables of quantiles of these statistics are also provided. The power of the proposed test is studied and compared to that of other well-known tests also using simulation. The proposed test is more powerful in most of the considered cases. Acceptance regions for the PP, QQ, and Michael's stabilized probability plots are derived, which enable one to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an application in quality control is presented as illustration.

Keywords:

• Kolmogorov–Smirnov test
• Monte Carlo simulation
• PP
• QQ
• and stabilized probability plots
• Quality control

Mathematics Subject Classification:

• Primary 65C10
• Secondary 60E05

Acknowledgments

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, X094 from the Universidad de Buenos Aires, and PIP5505 from CONICET grants, Argentina and by FONDECYT 1080326 and DIPUV 29-2006 grants, Chile.