A Goodness of Fit Tests Based on the Partial Kullback-Leibler Information with the Type II Censored Data

Goodness of fit test statistics based on the information discrepancy have been shown to perform very well (Vasicek 1976, Dudewicz and van der Meulen 1981, Chandra et al 1982, Gohkale 1983, Arizona and Ohta 1989, Ebrahimi et al 1992, etc). Although the test is well defined for the non-censored case, censored case has not been discussed in the literature. Therefore we consider a goodness of fit test based on the partial Kullback-Leibler(KL) information with the type II censored data. We derive the partial KL information of the null distribution function and a nonparametric distribution function, and establish a goodness of fit test statistic. We consider the exponential and normal distributions and made Monte Calro simulations to compare the test statistics with some existing tests.