Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Default Bayesian testing equality of scale parameters in several inverse Gaussian distributions

  • Kang, Sang Gil (Department of Computer and Data Information, Sangji University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University) ;
  • Lee, Woo Dong (Department of Data Management, Daegu Haany University)
  • Received : 2015.02.26
  • Accepted : 2015.04.20
  • Published : 2015.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

Keywords

References

  1. Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means : Bayesian analysis with reference priors. Journal of the American Statistical Association, 84, 200-207. https://doi.org/10.1080/01621459.1989.10478756
  2. Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). Bayesian Statistics IV, edited by J. M. Bernardo, et al., Oxford University Press, Oxford, 35-60.
  3. Berger, J. O. and Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109-122. https://doi.org/10.1080/01621459.1996.10476668
  4. Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: the median intrinsic Bayes factor. Sankya B, 60, 1-18.
  5. Berger, J. O. and Pericchi, L. R. (2001). Objective Bayesian methods for model selection: introduction and comparison (with discussion). In Model Selection, Institute of Mathematical Statistics Lecture Notes-Monograph Series, Vol. 38, edited by P. Lahiri, 135-207, Beachwood Ohio.
  6. Chang, M., You, X., Wen, M. (2012). Testing the homogeneity of inverse Gaussian scale-like parameters. Statistics & Probability Letters, 82, 1755-1760. https://doi.org/10.1016/j.spl.2012.05.013
  7. Chhikara, R. S. and Folks, L. (1989). The inverse Gaussian distribution; theory, methodology and applications, Marcel Dekker, New York.
  8. Kang, S. G., Kim, D. H. and Lee, W. D. (2013). Default Bayesian testing for the scale parameters in two parameter exponential distributions. Journal of the Korean Data & Information Science Society, 24, 949-957. https://doi.org/10.7465/jkdi.2013.24.4.949
  9. Kang, S. G., Kim, D. H. and Lee, W. D. (2014). Default Bayesian testing for the scale parameters in the half logistic distributions. Journal of the Korean Data & Information Science Society, 25, 465-472. https://doi.org/10.7465/jkdi.2014.25.2.465
  10. Krishnamoorthy, K. and Tian, L. L. (2008). Inferences on the difference and ratio of the means of two inverse Gaussian distributions. Journal of Statistical Planning and Inference, 138, 2082-2089. https://doi.org/10.1016/j.jspi.2007.09.005
  11. Liu, X. H. and He, D. J. (2013) Testing homogeneity of inverse Gaussian scale parameters based on generalized likelihood ratio. Communications in Statistics-Simulation and Computation, 42, 382-392. https://doi.org/10.1080/03610918.2011.650257
  12. Ma, C. X. and Tian, L. L. (2009) A parametric bootstrap approach for testing equality of inverse Gaussian means under heterogeneity. Communications in Statistics-Simulation and Computation, 38, 1153-1160. https://doi.org/10.1080/03610910902833470
  13. Mudholkar, G. S. and Tian, L. (2002). An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit tests. Journal of Statistical Planning and Inference, 102, 211-221. https://doi.org/10.1016/S0378-3758(01)00099-4
  14. O'Hagan, A. (1995). Fractional Bayes factors for model comparison (with discussion). Journal of Royal Statistical Society B, 57, 99-118.
  15. O'Hagan, A. (1997). Properties of intrinsic and fractional Bayes factors. Test, 6, 101-118. https://doi.org/10.1007/BF02564428
  16. Sadooghi-Alvandi, S. M. and Malekzadeh, A. (2013). A note on testing homogeneity of the scale parameters of several inverse Gaussian distributions. Statistics & Probability Letters, 83, 1844-1848. https://doi.org/10.1016/j.spl.2013.04.019
  17. Seshadri, V. (1999). The inverse Gaussian distribution; statistical theory and applications, Springer Verlag, New York.
  18. Spiegelhalter, D. J. and Smith, A. F. M. (1982). Bayes factors for linear and log-linear models with vague prior information. Journal of Royal Statistical Society B, 44, 377-387.
  19. Tian, L. L. (2006) Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable. Computational Statistics & Data Analysis, 51, 1156-1162. https://doi.org/10.1016/j.csda.2005.11.012
  20. Ye, R. D., Ma, T. F. and Wang, S. G. (2010). Inferences on the common mean of several inverse Gaussian populations. Computational Statistics & Data Analysis, 54, 906-915. https://doi.org/10.1016/j.csda.2009.09.039

Cited by

  1. Bayesian estimation for Rayleigh models vol.28, pp.4, 2015, https://doi.org/10.7465/jkdi.2017.28.4.875