Skip to main content

Classical and Bayesian Goodness-of-fit Tests for the Exponential Model: A Comparative Study

  • Conference paper
Computational Science and Its Applications – ICCSA 2014 (ICCSA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8581))

Included in the following conference series:

  • 2388 Accesses

Abstract

Most common statistical methodologies assume a parametric model for the data and inference is made based on that assumption. If the model does not fit the data, the resulting inference will be mislead. Thus, evaluation of the fitting of a proposed parametric statistical model to a given dataset becomes an important issue.

In several practical situations, namely in reliability and life sciences problems, the exponential model has been widely used and several classical tests were already proposed for its fitting evaluation. In this work we suggest two Bayesian tests when an exponential model is proposed to describe the data, and using a simulation study, we compare their power with the classical ones.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D’Agostino, R.B., Stephens, M.A.: Goodness-of-fit Techniques. Marcel Dekker, New York (1986)

    MATH  Google Scholar 

  2. Baringhaus, L., Henze, N.: A class of consistent tests for exponentiality based on the empirical Laplace transform. Ann. Inst. Statist. Math. 43, 551–564 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baringhaus, L., Henze, N.: Tests of fit for exponentiality based on a characterization via the mean residual life function. Statist. Paper 41, 225–236 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Choi, B., Kim, K., Song, S.H.: Goodness of fit test for exponentiality based on Kullback-Leibler information. Comm. Statist. Simulation Comput. 33(2), 525–536 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Henze, N., Meintanis, S.: Recent and classical tests for exponentiality: A partial review with comparisons. Metrika 61, 29–45 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Grané, A., Fortiana, J.: A directional test of exponentiality based on maximum correlations. Metrika 73, 255–274 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gelman, A., Meng, X.L., Stern, H.: Posterior predictive assesssment of model fitness via realized discrepancies (with discussion). Statist. Sinica 6, 733–807 (1996)

    MathSciNet  MATH  Google Scholar 

  8. Robins, J.M., Vaart, A., van der Ventura, V.: Asymptotic distribution of p-values in composite null models. J. Amer. Statist. Assoc. 95, 1143–1159 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bayarri, M.J., Berger, J.O.: P-values for composite null models. J. Amer. Statist. Assoc. 95, 1127–1142 (2000)

    MathSciNet  MATH  Google Scholar 

  10. Hjort, N.L., Dahl, F.A., Steinbakk, G.H.: Post-processing posterior predictive p-values. J. Amer. Statist. Assoc. 101, 1157–1174 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Johnson, V.E.: A Bayesian chi-squared test for goodness-of-fit. Ann. Statist. 32(6), 2361–2384 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Johnson, V.E.: Bayesian model assessment using pivotal quantities. Bayesian Analysis 2, 719–734 (2007)

    Article  MathSciNet  Google Scholar 

  13. Hjort, N.L., Holmes, C., Müller, P., Walker, S.G.: Bayesian Nonparametrics. Cambridge University Press, New York (2010)

    Book  MATH  Google Scholar 

  14. Verdinelli, I., Wasserman, L.: Bayesian goodness-of-fit testing using infinite-dimensional exponential families. Ann. Statist. 26, 1215–1241 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Berger, J.O., Guglielmi, A.: Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. J. Amer. Statist. Assoc. 96, 174–184 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tokdar, S.T., Martin, R.: Bayesian test of normality versus a Dirichlet process mixture alternative. ArXiv e-prints (2011)

    Google Scholar 

  17. Lavine, M.: Some aspects of Polya tree distributions for statistical modeling. Ann. Statist. 20, 1222–1235 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lavine, M.: More aspects of Polya tree distributions for statistical modeling. Ann. Statist. 22, 1161–1176 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hanson, T., Johnson, W.: Modeling regression errors with a mixture of Polya trees. J. Amer. Statist. Assoc. 97, 1020–1033 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hanson, T.: Inference for mixture of finite Polya tree models. J. Amer. Statist. Assoc. 101, 1548–1565 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Schervish, M.J.: Theory os Statistic. Springer, New York (1995)

    Book  Google Scholar 

  22. Cox, D., Oakes, D.: Analysis of Survival Data. Chapman and Hall, New York (1984)

    Google Scholar 

  23. Epps, T., Pulley, L.: A test for exponentiality vs. monotone hazard alternatives derived from the empirical characteristic function. J. R. Stat. Soc. Ser. B 48(2), 206–213 (1986)

    MathSciNet  MATH  Google Scholar 

  24. Anderson, T.W., Darling, D.A.: A test of goodness-of-fit. J. Amer. Statist. Assoc. 49, 765–769 (1954)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Polidoro, M.J., Magalhães, F.J., Turkman, M.A.A. (2014). Classical and Bayesian Goodness-of-fit Tests for the Exponential Model: A Comparative Study. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8581. Springer, Cham. https://doi.org/10.1007/978-3-319-09150-1_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09150-1_35

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09149-5

  • Online ISBN: 978-3-319-09150-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics