Computational Statistics

, Volume 32, Issue 4, pp 1241–1283 | Cite as

An ‘apples to apples’ comparison of various tests for exponentiality

  • J. S. Allison
  • L. Santana
  • N. Smit
  • I. J. H. Visagie
Original Paper
  • 147 Downloads

Abstract

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.

Keywords

Bootstrap Exponential distribution Goodness-of-fit testing Tuning parameter 

Notes

Acknowledgements

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • J. S. Allison
    • 1
  • L. Santana
    • 1
  • N. Smit
    • 1
  • I. J. H. Visagie
    • 2
  1. 1.Unit for Business Mathematics and InformaticsNorth-West UniversityPotchefstroomSouth Africa
  2. 2.Department of Statistics, Faculty of Natural and Agricultural SciencesUniversity of PretoriaPretoriaSouth Africa

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