The Shapiro-Wilk Test for Exponentiality Based on Censored Data

Abstract

Abstract In this article we present a modification of the Shapiro-Wilk (1972) exponentiality test when the sample is censored. The test statistic is constructed by using the normalized waiting times based on the sample data, and is shown to have the same null distribution as the uncensored case with a corresponding reduction in sample size. Stephens's (1978) modification of the Shapiro-Wilk statistic for known origin is also modified, to allow censoring in the sample. Again, the test is constructed using the normalized waiting times; it also has the same null distribution as the uncensored case, with a reduction in the sample size. We compare the power of our test with the power of the Brain and Shapiro (1983) regression tests, using Monte Carlo simulation. Our test compares favorably to the regression test, and it often does better in the case of left censoring. We then demonstrate how our results may be used in a test for uniformity, using the probability integral transformation. Finally, we give an exp...