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

Claudia Castro-Kuriss, Diana M. Kelmansky, VICTOR ELISEO LEIVA SANCHEZ, Elena J. Martínez

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8 Scopus citations

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.

Original languageEnglish
Pages (from-to)1193-1211
Number of pages19
JournalJournal of Applied Statistics
Volume37
Issue number7
DOIs
StatePublished - 1 Jul 2010

Keywords

  • Kolmogorov-Smirnov test
  • Maximum likelihood and Gupta's estimators
  • Monte Carlo simulation
  • PP, QQ and stabilized probability plots

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