The Shapiro-Wilk Test for Exponentiality Based on Censored Data
本文改进了Shapiro-Wilk指数性检验，使其适用于删失数据，通过归一化等待时间构造检验统计量，并证明其与无删失情况有相同的零分布，模拟显示该检验在左删失时优于回归检验。
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 explicit expression for the null distribution of the Shapiro-Wilk test in the neighborhood of its upper tail.