Goodness-of-Fit Tests Based on Spacings for Progressively Type-II Censored Data From a General Location-Scale Distribution

There has been extensive research on goodness-of-fit procedures for testing whether or not a sample comes from a specified distribution. These goodness-of-fit tests range from graphical techniques, to tests which exploit characterization results for the specified underlying model. In this article, we propose a goodness-of-fit test for the location-scale family based on progressively Type-II censored data. The test statistic is based on sample spacings, and generalizes a test procedure proposed by Tiku [1]. The null distribution of the test statistic is shown to be approximated closely by a $s$-normal distribution. However, in certain situations it would be better to use simulated critical values instead of the $s$-normal approximation. We examine the performance of this test for the $s$-normal and extreme-value (Gumbel) models against different alternatives through Monte Carlo simulations. We also discuss two methods of power approximation based on $s$-normality, and compare the results with those obtained by simulation. Results of the simulation study for a wide range of sample sizes, censoring schemes, and different alternatives reveal that the proposed test has good power properties in detecting departures from the $s$-normal and Gumbel distributions. Finally, we illustrate the method proposed here using real data from a life-testing experiment. It is important to mention here that this test can be extended to multi-sample situations in a manner similar to that of Balakrishnan [2].