DOI QR코드

DOI QR Code

Default Bayesian one sided testing for the shape parameter in the log-logistic distribution

  • Kang, Sang Gil (Department of Computer and Data Information, Sangji University)
  • Received : 2015.09.15
  • Accepted : 2015.10.23
  • Published : 2015.11.30

Abstract

This paper deals with the problem of testing on the shape parameter in the log-logistic distribution. We propose default Bayesian testing procedures for the shape parameter 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. We can solve the this problem by the intrinsic Bayes factor and the fractional Bayes factor. 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. 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. Ali, M. M. and Khan, A. H. (1987). On order statistics from the log-logistic distribution. Journal of Statistical Planning and Inference, 17, 103-108. https://doi.org/10.1016/0378-3758(87)90104-2
  3. Balakrishnan, N. and Malik, H. J. (1987). Moments of order statistics form truncated log-logistic distribution. Journal of Statistical Planning and Inference, 17, 251-267. https://doi.org/10.1016/0378-3758(87)90117-0
  4. Bennett, S. (1983). Log-logistic regression models for survival data. Journal of Royal Statistical Society, C, 32, 165-171.
  5. 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
  6. 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.
  7. Berger, J. O. and Mortera, J. (1999). Defaut Bayes factor for one-sided hypothesis testing. Journal of the American Statistical Association, 94, 542-554. https://doi.org/10.1080/01621459.1999.10474149
  8. 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
  9. Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: The median intrinsic Bayes factor. Sankya B, 60, 1-18.
  10. 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, 135-207.
  11. Chen, Z. (1997). Exact confidence interval for the shape parameter of a log-logistic distribution. Journal of Statistical Computation and Simulation, 56, 193-211. https://doi.org/10.1080/00949659708811789
  12. Dmochowski, J. (1996). Intrinsic priors via Kullback-Leibler geometry. Bayesian Statistics V, edited by J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, Oxford University Press, Oxford, 543-549.
  13. 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.
  14. Fisk P. R. (1961). The graduation of income distributions. Econometrica, 29, 171-185. https://doi.org/10.2307/1909287
  15. Franco, M. A. P. (1984). A log logistic model for survival time with covariates. Biometrika, 71, 621-623. https://doi.org/10.1093/biomet/71.3.621
  16. 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
  17. 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
  18. 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
  19. 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
  20. Lawless, J. F. (1982). Statistical models and methods for lifetime data, John Wiley and Sons, New York.
  21. O'Hagan, A. (1995). Fractional Bayes factors for model comparison (with discussion). Journal of Royal Statistical Society B, 57, 99-118.
  22. O'Hagan, A. (1997). Properties of intrinsic and fractional Bayes factors. Test, 6, 101-118. https://doi.org/10.1007/BF02564428
  23. Ragab, A. and Green, J. (1984). On order statistics from the log-logistic distribution and their properties. Communication in Statistics-Theory and Methods, 13, 2713-2724. https://doi.org/10.1080/03610928408828855
  24. Robson, A. and Reed, D. (1999). Statistical procedures for flood frequency estimation. Flood estimation handbook, 3, Institute of Hydrology, Wallingford, UK.
  25. 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
  26. 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.