An ‘apples to apples’ comparison of various tests for exponentiality
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The exponential distribution is a popular model both in practice and in theoretical work. As a result, a multitude of tests based on varied characterisations have been developed for testing the hypothesis that observed data are realised from this distribution. Many of the recently developed tests contain a tuning parameter, usually appearing in a weight function. In this paper we compare the powers of 20 tests for exponentiality—some containing a tuning parameter and some that do not. To ensure a fair ‘apples to apples’ comparison between each of the tests, we employ a data-dependent choice of the tuning parameter for those tests that contain these parameters. The comparisons are conducted for various samples sizes and for a large number of alternative distributions. The results of the simulation study show that the test with the best overall power performance is the Baringhaus and Henze test, followed closely by the test by Henze and Meintanis; both tests contain a tuning parameter. The score test by Cox and Oakes performs the best among those tests that do not include a tuning parameter.
KeywordsBootstrap Exponential distribution Goodness-of-fit testing Tuning parameter
The first author thanks the National Research Foundation of South Africa for financial support. The authors would also like to thank the Referee and Associate Editor for their constructive and insightful comments that led to an improvement of the paper.
- Balakrishnan N, Ng HKT, Kannan N (2002) A test of exponentiality based on spacings for progressively Type-II censored data. In: Goodness-of-fit tests and model validity, chap 8. Birkhäuser, Boston, pp 89–111Google Scholar
- Cox DR, Oakes D (1984) Analysis of survival data. Chapman and Hall, LondonGoogle Scholar
- Kotze S, Johnson NL (1983) Encyclopedia of statistical sciences, vol 3. Wiley, New YorkGoogle Scholar
- Novikov A, Pusev R, Yakovlev M (2013) Exptest: tests for exponentiality. http://CRAN.R-project.org/package=exptest, R Package Version 1.2
- R Core Team (2013) R: A language and environment for statistical computing. http://www.R-project.org/
- Taufer E (2000) A new test for exponentiality against omnibus alternatives. Stoch Model Appl 3:23–36Google Scholar