TY - JOUR
T1 - On a goodness-of-fit test for normality with unknown parameters and type-II censored data
AU - Castro-Kuriss, Claudia
AU - Kelmansky, Diana M.
AU - Leiva, Víctor
AU - Martínez, Elena J.
N1 - Funding Information:
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.
PY - 2010/7
Y1 - 2010/7
N2 - 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.
AB - 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.
KW - Kolmogorov-Smirnov test
KW - Maximum likelihood and Gupta's estimators
KW - Monte Carlo simulation
KW - PP, QQ and stabilized probability plots
UR - http://www.scopus.com/inward/record.url?scp=77954121998&partnerID=8YFLogxK
U2 - 10.1080/02664760902984626
DO - 10.1080/02664760902984626
M3 - Article
AN - SCOPUS:77954121998
SN - 0266-4763
VL - 37
SP - 1193
EP - 1211
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
IS - 7
ER -