Janssen, Paul; Swanepoel, Jan; Veraverbeke, Noël New tests for exponentiality against new better than used in \(p\)th quantile. (English) Zbl 1154.62037 J. Nonparametric Stat. 21, No. 1, 85-97 (2009). 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. Cited in 5 Documents 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 Keywords:characterisation; exponential distribution; hazard rate function; new better than used in \(p\)th quantile; testing; \(U\)-quantile; Winsorised mean PDFBibTeX XMLCite \textit{P. Janssen} et al., J. Nonparametric Stat. 21, No. 1, 85--97 (2009; Zbl 1154.62037) Full Text: DOI References: [1] Lai C.-D., Stochastic Ageing and Dependence for Reliability (2006) [2] Haines A. L., Reliability and Biometry pp 47– (1974) [3] DOI: 10.1287/opre.32.3.668 · Zbl 0558.62084 · doi:10.1287/opre.32.3.668 [4] DOI: 10.1080/03610928308828518 · Zbl 0522.62083 · doi:10.1080/03610928308828518 [5] Song J.-K., Sankhya Ser. A 57 pp 333– (1995) [6] DOI: 10.1016/0378-3758(88)90036-5 · Zbl 0662.62051 · doi:10.1016/0378-3758(88)90036-5 [7] Helmers R., Exploring the Limits of Bootstrap pp 145– (1992) [8] DOI: 10.1002/9780470316481 · Zbl 0538.62002 · doi:10.1002/9780470316481 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.