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On a goodness-offit test for censored data from a location-scale distribution with applications

In this article, we propose a goodness-of-fit test for singly Type II censored samples from a general location-scale distribution with unknown parameters. The test is a generalization to censored samples of that proposed by Michael (1983), which is based on the empirical distribution function and a variance stabilizing transformation. Acceptance regions for the probability-probability and Michael’s stabilized probability plots are derived. These regions allow us the possibility of visualizing which data contribute to the decision of rejecting the null hypothesis. We consider the exponential distribution with unknown location and scale parameters as a particular case. We study the distribution of the test statistic under the null hypothesis by Monte Carlo methods. The power of the test is also estimated and compared by simulations to several distributions for the alternative hypothesis and for different sample sizes and censoring proportions. We implement the obtained results in R language. Finally, we illustrate the proposed results by using reliability real data sets.