IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i4d10.1007_s00180-017-0733-3.html
   My bibliography  Save this article

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

Author

Listed:
  • J. S. Allison

    (North-West University)

  • L. Santana

    (North-West University)

  • N. Smit

    (North-West University)

  • I. J. H. Visagie

    (University of Pretoria)

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.

Suggested Citation

  • J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0733-3
    DOI: 10.1007/s00180-017-0733-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-017-0733-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-017-0733-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jovanović, Milan & Milošević, Bojana & Nikitin, Ya. Yu. & Obradović, Marko & Volkova, K. Yu., 2015. "Tests of exponentiality based on Arnold–Villasenor characterization and their efficiencies," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 100-113.
    2. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    3. Baringhaus, L. & Henze, N., 2008. "A new weighted integral goodness-of-fit statistic for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1006-1016, June.
    4. Sreenivasa Rao Jammalamadaka & Emanuele Taufer, 2001. "Testing Exponentiality by comparing the Empirical," Quaderni DISA 053, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    5. Sreenivasa Rao Jammalamadaka & Emanuele Taufer, 2002. "The use of Mean Residual Life in testing departures from Esxponentiality," Quaderni DISA 071, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    6. V. Zardasht & S. Parsi & M. Mousazadeh, 2015. "On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality," Statistical Papers, Springer, vol. 56(3), pages 677-688, August.
    7. Jin Zhang, 2002. "Powerful goodness‐of‐fit tests based on the likelihood ratio," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 281-294, May.
    8. Bernhard Klar, 2001. "Goodness-Of-Fit Tests for the Exponential and the Normal Distribution Based on the Integrated Distribution Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 338-353, June.
    9. Aurea Grané & Josep Fortiana, 2011. "A directional test of exponentiality based on maximum correlations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 255-274, March.
    10. P. Wong & S. Wong, 1979. "An extremal quotient test for exponential distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 1-4, December.
    11. Ludwig Baringhaus & Norbert Henze, 1991. "A class of consistent tests for exponentiality based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 551-564, September.
    12. Jammalamadaka, S.R.S. Rao & Goria, M. N., 2004. "A test of goodness-of-fit based on Gini's index of spacings," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 177-187, June.
    13. Y. A. S. Hegazy & J. R. Green, 1975. "Some New Goodness‐Of‐Fit Tests Using Order Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(3), pages 299-308, November.
    14. Haywood, John & Khmaladze, Estate, 2008. "On distribution-free goodness-of-fit testing of exponentiality," Journal of Econometrics, Elsevier, vol. 143(1), pages 5-18, March.
    15. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Steffen Betsch & Bruno Ebner, 2020. "Testing normality via a distributional fixed point property in the Stein characterization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 105-138, March.
    2. Steffen Betsch & Bruno Ebner, 2019. "A new characterization of the Gamma distribution and associated goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 779-806, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bojana Milošević & Marko Obradović, 2016. "New class of exponentiality tests based on U-empirical Laplace transform," Statistical Papers, Springer, vol. 57(4), pages 977-990, December.
    2. M. Cockeran & S. G. Meintanis & L. Santana & J. S. Allison, 2021. "Goodness-of-fit testing of survival models in the presence of Type–II right censoring," Computational Statistics, Springer, vol. 36(2), pages 977-1010, June.
    3. Baringhaus, L. & Henze, N., 2008. "A new weighted integral goodness-of-fit statistic for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1006-1016, June.
    4. L. Ndwandwe & J. S. Allison & L. Santana & I. J. H. Visagie, 2023. "Testing for the Pareto type I distribution: a comparative study," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 215-256, August.
    5. Ruhul Ali Khan & Dhrubasish Bhattacharyya & Murari Mitra, 2021. "Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives," Statistical Papers, Springer, vol. 62(6), pages 3015-3045, December.
    6. Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    7. Gerrit Lodewicus Grobler & Elzanie Bothma & James Samuel Allison, 2022. "Testing for the Rayleigh Distribution: A New Test with Comparisons to Tests for Exponentiality Based on Transformed Data," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    8. Haywood, John & Khmaladze, Estate, 2008. "On distribution-free goodness-of-fit testing of exponentiality," Journal of Econometrics, Elsevier, vol. 143(1), pages 5-18, March.
    9. Simos Meintanis & Bojana Milošević & Marko Obradović, 2023. "Bahadur efficiency for certain goodness-of-fit tests based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(7), pages 723-751, October.
    10. Simos G. Meintanis & Christos K. Papadimitriou, 2022. "Goodness--of--fit tests for stochastic frontier models based on the characteristic function," Journal of Productivity Analysis, Springer, vol. 57(3), pages 285-296, June.
    11. Simos G. Meintanis & Bojana Milošević & Marko Obradović, 2020. "Goodness-of-fit tests in conditional duration models," Statistical Papers, Springer, vol. 61(1), pages 123-140, February.
    12. L. Baringhaus & N. Henze, 2017. "Cramér–von Mises distance: probabilistic interpretation, confidence intervals, and neighbourhood-of-model validation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 167-188, April.
    13. Sreenivasa Rao Jammalamadaka & Emanuele Taufer, 2002. "The use of Mean Residual Life in testing departures from Esxponentiality," Quaderni DISA 071, Department of Computer and Management Sciences, University of Trento, Italy, revised 12 Sep 2003.
    14. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
    15. Banerjee, Shuvadeep, 2008. "A distribution free goodness of fit test for a stochastically ordered alternative," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2868-2875, December.
    16. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    17. Fernández de Marcos Giménez de los Galanes, Alberto, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    19. P. Sankaran & N. Midhu, 2016. "Testing exponentiality using mean residual quantile function," Statistical Papers, Springer, vol. 57(1), pages 235-247, March.
    20. Asok K. Nanda & Shovan Chowdhury, 2021. "Shannon's Entropy and Its Generalisations Towards Statistical Inference in Last Seven Decades," International Statistical Review, International Statistical Institute, vol. 89(1), pages 167-185, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0733-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.