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 for scale parameters in the log-logistic 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 Asset Management, Daegu Haany University)
  • Received : 2015.06.27
  • Accepted : 2015.11.18
  • Published : 2015.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the problem of testing on the equality of the scale parameters in the log-logistic distributions. We propose default Bayesian testing procedures for the scale 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 factor under the reference priors. To justify proposed procedures, a simulation study is provided and also, an example is given.

Keywords

References

  1. Ahmad, M. I., Sinclair, C. D. and Werritty, A. (1988). Log-logistic flood frequency analysis. Journal of Hydrology, 98, 205-212. https://doi.org/10.1016/0022-1694(88)90015-7
  2. Bennett, S. (1983). Log-logistic regression models for survival data. Journal of Royal Statistical Society C, 32, 165-171.
  3. 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
  4. 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.
  5. 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
  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, Vol 38, edited by P. Lahiri, 135-207, Beachwood Ohio.
  7. Dey, A. K. and Kundu, D. (2010). Discriminating between the log-normal and log-logistic distributions. Communications in Statistics-Theory and Methods, 39, 280-292.
  8. Fisk P. R. (1961). The graduation of income distributions. Econometrica, 29, 171-185. https://doi.org/10.2307/1909287
  9. Geskus, R. B. (2001). Methods for estimating the AIDS incubation time distribution when data of seroconversion is censored. Statistics in Medicine, 20, 795-812. https://doi.org/10.1002/sim.700
  10. 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
  11. Kang, S. G., Kim, D. H. and Lee, W. D. (2014a). Noninformative priors for the log-logistic distribution. Journal of the Korean Data & Information Science Society, 25, 227-235. https://doi.org/10.7465/jkdi.2014.25.1.227
  12. Kang, S. G., Kim, D. H. and Lee, W. D. (2014b). 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
  13. Lawless, J. F. (1982). Statistical models and methods for lifetime data, John Wiley and Sons, New York.
  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. Robson, A. and Reed, D. (1999). Statistical procedures for flood frequency estimation. Flood estimation handbook, 3, Institute of Hydrology, Wallingford, UK.
  17. Shoukri, M. M., Mian I. U. M., and Tracy, C. (1988). Sampling properties of estimators of log-logistic distribution with application to Canadian precipitation data. Canadian Journal of Statistics, 16, 223-236. https://doi.org/10.2307/3314729
  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.

Cited by

  1. Estimation of Gini-Simpson index for SNP data vol.28, pp.6, 2015, https://doi.org/10.7465/jkdi.2017.28.6.1557