DOI QR코드

DOI QR Code

Default Bayesian testing for the equality of the scale parameters of several inverted exponential 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 : 2014.06.07
  • Accepted : 2014.07.21
  • Published : 2014.07.31

Abstract

This article deals with the problem of testing the equality of the scale parameters of several inverted exponential distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis 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. Abouammoh, A. M. and Alshingiti, A. M. (2009). Reliability estimation of generalized inverted exponential distribution. Journal of Statistical Computation and Simulation, 79, 1301-1315. https://doi.org/10.1080/00949650802261095
  2. Bertolino, F., Racugno, W. and Moreno, E. (2000). Bayesian model selection approach to analysis of variance under heteroscedasticity. The Statistician, 49, 503-517.
  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). In 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, Beachwood Ohio, 135-207.
  7. Dey, S. (2007). Inverted exponential distribution as a life time distribution model from a Bayesian viewpoint. Data Science Journal, 6, 107-113. https://doi.org/10.2481/dsj.6.107
  8. Kang, S. G., Kim, D. H. and Lee, W. D. (2008). Bayesian model selection for inverse Gaussian populations with heterogeneity. Journal of the Korean Data & Information Science Society, 19, 621-634.
  9. Kang, S. G., Kim, D. H. and Lee, W. D. (2011). Default Bayesian testing for the bivariate normal correlation coecient. Journal of the Korean Data & Information Science Society, 22, 1007-1016.
  10. Killer, A. Z. and Kamath, A. R. (1982). Reliability analysis of CNC machine tools. Reliability Engineering, 3, 449-473. https://doi.org/10.1016/0143-8174(82)90036-1
  11. Lee, W. D. and Kang, S. G. (2008). Bayesian multiple hypotheses testing for Poisson mean. Journal of the Korean Data & Information Science Society, 19, 331-341.
  12. Lin, C., Duran, B. S. and Lewis, T. O. (1989). Inverted gamma as a life distribution. Microelectronics Reliability, 29, 619-626. https://doi.org/10.1016/0026-2714(89)90352-1
  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. Singh, S. K., Singh, U. and Kumar, D. (2013). Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors. Journal of Statistical Computation and Simulation, 83, 2258-2269. https://doi.org/10.1080/00949655.2012.690156
  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.