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New tests for exponentiality against new better than used in \(p\)th quantile. (English) Zbl 1154.62037

Summary: A new characterisation of the exponential distribution in a wide class of new better than used in \(p\)th quantile (NBU\(p\)) lifetime distributions is presented. This leads to new classes of scale-free goodness-of-fit tests for exponentiality against NBU\(p\) alternatives. The limiting distributions of the test statistics under the null and alternative hypotheses are derived and the tests are shown to be consistent against NBU\(p\) alternatives. Pitman efficacies are calculated and a limited Monte Carlo study is conducted to compare the tests with regard to power for small and moderate sample sizes against a range of alternative distributions. On the basis of overall good performance and ease of computation, a member of the class of test statistics which is based on the sample Winsorised mean is recommended as a scale-free goodness-of-fit test for the exponential distribution.

MSC:

62G10 Nonparametric hypothesis testing
62E10 Characterization and structure theory of statistical distributions
62N03 Testing in survival analysis and censored data
62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
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