IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v57y2016i4d10.1007_s00362-016-0818-z.html
   My bibliography  Save this article

New class of exponentiality tests based on U-empirical Laplace transform

Author

Listed:
  • Bojana Milošević
  • Marko Obradović

Abstract

In this paper, a new class of goodness of fit tests for exponential distribution is proposed. The tests use the equidistribution characterizations of exponential distribution. Based on the U-empirical Laplace transforms of equidistributed statistics, test statistics of the integral type are formed. They are U-statistics with estimated parameters. Their asymptotic properties are derived. Two families of exponentiality tests from this class, based on two selected characterizations, are presented. The approximate Bahadur efficiency is used to assess their quality. Finally, their simulated powers are calculated and the tests are compared with different exponentiality tests.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0818-z
    DOI: 10.1007/s00362-016-0818-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0818-z
    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/s00362-016-0818-z?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. Henze, Norbert & Nikitin, Yakov & Ebner, Bruno, 2009. "Integral distribution-free statistics of Lp-type and their asymptotic comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3426-3438, July.
    3. Nora Gürtler & Norbert Henze, 2000. "Goodness-of-Fit Tests for the Cauchy Distribution Based on the Empirical Characteristic Function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 267-286, June.
    4. 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.
    5. 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.
    6. Helena Jansen Van Rensburg & Jan Swanepoel, 2008. "A class of goodness-of-fit tests based on a new characterization of the exponential distribution," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 539-551.
    7. Simos Meintanis & George Iliopoulos, 2003. "Tests of fit for the Rayleigh distribution based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 137-151, March.
    8. Yakov Y. Nikitin & Irina Peaucelle, 2004. "Efficiency and local optimality of nonparametric tests based on U- and V-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 185-200.
    9. 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.
    10. Norbert Henze & Bernhard Klar, 2002. "Goodness-of-Fit Tests for the Inverse Gaussian Distribution Based on the Empirical Laplace Transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(2), pages 425-444, June.
    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. 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.
    2. Marija Cuparić & Bojana Milošević, 2022. "New characterization-based exponentiality tests for randomly censored data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 461-487, June.

    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. 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.
    2. 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.
    3. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.
    4. 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.
    5. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.
    6. 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.
    7. 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.
    8. 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.
    9. E. Bothma & J. S. Allison & I. J. H. Visagie, 2022. "New classes of tests for the Weibull distribution using Stein’s method in the presence of random right censoring," Computational Statistics, Springer, vol. 37(4), pages 1751-1770, September.
    10. 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.
    11. 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.
    12. James Allison & Bojana Milošević & Marko Obradović & Marius Smuts, 2022. "Distribution-free goodness-of-fit tests for the Pareto distribution based on a characterization," Computational Statistics, Springer, vol. 37(1), pages 403-418, March.
    13. 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.
    14. Milošević, B. & Obradović, M., 2016. "Characterization based symmetry tests and their asymptotic efficiencies," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 155-162.
    15. 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.
    16. Baringhaus, Ludwig & Gaigall, Daniel, 2015. "On an independence test approach to the goodness-of-fit problem," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 193-208.
    17. 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.
    18. 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.
    19. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    20. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.

    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:stpapr:v:57:y:2016:i:4:d:10.1007_s00362-016-0818-z. 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.