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Recent and classical tests for exponentiality: a partial review with comparisons

Author

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  • Norbert Henze
  • Simos G. Meintanis

Abstract

A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramér-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramér-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study. Copyright Springer-Verlag 2005

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metrik:v:61:y:2005:i:1:p:29-45
    DOI: 10.1007/s001840400322
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    Citations

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    Cited by:

    1. Atle Oglend & Frank Asche, 2016. "Cyclical non-stationarity in commodity prices," Empirical Economics, Springer, vol. 51(4), pages 1465-1479, December.
    2. 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.
    3. repec:bla:biomet:v:73:y:2017:i:2:p:687-695 is not listed on IDEAS
    4. Bojana Milošević, 2016. "Asymptotic efficiency of new exponentiality tests based on a characterization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 221-236, February.
    5. Bojana Milošević, 2016. "Asymptotic efficiency of new exponentiality tests based on a characterization," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 221-236, February.
    6. repec:spr:advdac:v:13:y:2019:i:2:d:10.1007_s11634-018-0309-2 is not listed on IDEAS
    7. M. Anis, 2011. "Comments on “Testing for NBUL using goodness of fit approach with applications” (Statistical Papers (2010) 51: 27–40, DOI 10.1007/s00362-007-0113-0)," Statistical Papers, Springer, vol. 52(3), pages 743-747, August.
    8. T. Fischer & U. Kamps, 2013. "Power maps in goodness-of-fit testing," Computational Statistics, Springer, vol. 28(3), pages 1365-1382, June.
    9. Wang, Bing Xing, 2009. "Testing for the validity of the assumptions in the exponential step-stress accelerated life-testing model," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2702-2709, May.
    10. repec:taf:gnstxx:v:29:y:2017:i:2:p:167-188 is not listed on IDEAS
    11. 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.
    12. 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.
    13. repec:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0827-y is not listed on IDEAS
    14. 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.
    15. Hadi Alizadeh Noughabi & Narayanaswamy Balakrishnan, 2016. "Tests of goodness of fit based on Phi-divergence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(3), pages 412-429, March.
    16. repec:taf:gnstxx:v:20:y:2008:i:6:p:539-551 is not listed on IDEAS
    17. 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.
    18. repec:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0733-3 is not listed on IDEAS
    19. Meintanis, Simos G. & Tsionas, Efthimios, 2010. "Testing for the generalized normal-Laplace distribution with applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3174-3180, December.
    20. repec:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0567-8 is not listed on IDEAS
    21. 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.
    22. Roberts, Mark C., 2009. "Duration and characteristics of metal price cycles," Resources Policy, Elsevier, vol. 34(3), pages 87-102, September.

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