Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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Bayesian testing for the homogeneity of the shape parameters of several inverse Gaussian distributions

  • Lee, Woo Dong (Faculty of Medical Industry Convergence, Daegu Haany University) ;
  • Kim, Dal Ho (Department of Statistics, Kyungpook National University) ;
  • Kang, Sang Gil (Department of Computer and Data Information, Sangji University)
  • 투고 : 2016.04.25
  • 심사 : 2016.05.24
  • 발행 : 2016.05.31
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초록

We develop the testing procedures about the homogeneity of the shape parameters of several inverse Gaussian distributions in our paper. We propose default Bayesian testing procedures for the shape parameters under the reference priors. The Bayes factor based on the proper priors gives the successful results for Bayesian hypothesis testing. For the case of the lack of information, the noninformative priors such as Jereys' prior or the reference prior can be used. Jereys' prior or the reference prior involves the undefined constants in the computation of the Bayes factors. Therefore under the reference priors, we develop the Bayesian testing procedures with the intrinsic Bayes factors and the fractional Bayes factor. Simulation study for the performance of the developed testing procedures is given, and an example for illustration is given.

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참고문헌

  1. Bai, Z. D., Wang, K. Y. and Wong, W. K. (2011) Mean-variance ratio test, a complement to coefficient of variation test and Sharpe ratio test. Statistics and Probability Letters, 81, 1078-1085 https://doi.org/10.1016/j.spl.2011.02.035
  2. 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
  3. Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). Bayesian Statistics IV, edited by J.M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, Oxford University Press, Oxford, 35-60.
  4. 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
  5. Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: The median intrinsic Bayes factor. Sankya B, 60, 1-18.
  6. 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, 38, edited by P. Lahiri, 135-207, Beachwood Ohio.
  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. (2004). Noninformative priors for the ratio of parameters in inverse Gaussian distribution. The Korean Journal of Applied Statistics, 17, 49-60. https://doi.org/10.5351/KJAS.2004.17.1.049
  9. 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 Korean Data & Information Science Society, 24, 949-957. https://doi.org/10.7465/jkdi.2013.24.4.949
  10. 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
  11. Kang, S. G., Kim, D. H. and Lee, W. D. (2015). Noninformative priors for the common shape parameter of several inverse Gaussian distributions. Journal of the Korean Data & Information Science Society, 26, 243-253. https://doi.org/10.7465/jkdi.2015.26.1.243
  12. Niu, C., Guo, X., Xu, W. and Zhu, L. (2014). Testing equality of shape parameters in several inverse Gaussian populations. Metrika, 77, 795-809. https://doi.org/10.1007/s00184-013-0465-5
  13. O'Hagan, A. (1995). Fractional Bayes factors for model comparison (with discussion). Journal of Royal Statistical Society B, 57, 99-118.
  14. O'Hagan, A. (1997). Properties of intrinsic and fractional Bayes factors. Test, 6, 101-118. https://doi.org/10.1007/BF02564428
  15. Seshadri, V. (1999). The inverse Gaussian distribution; statistical theory and applications, Springer Verlag, New York.
  16. 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.
  17. Tian, L. L. (2006) Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable. Computational Statistics and Data Analysis, 51, 1156-1162. https://doi.org/10.1016/j.csda.2005.11.012
  18. Ye, R. D., Ma, T. F. and Wang, S. G. (2010) Inferences on the common mean of several inverse Gaussian populations. Computational Statistics and Data Analysis, 54, 906-915. https://doi.org/10.1016/j.csda.2009.09.039