Journal of the Korean Data and Information Science Society

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

Reference priors for nonregular Pareto distribution

  • 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 : 2011.06.01
  • Accepted : 2011.07.15
  • Published : 2011.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we develop the reference priors for the scale and shape parameters in the nonregular Pareto distribution. We derive the reference priors as noninformative priors and prove the propriety of joint posterior distribution under the general priors including reference priors in the order of inferential importance. Through the simulation study, we compare the reference priors with respect to coverage probabilities of parameter of interest in a frequentist sense.

Keywords

References

  1. Arnold, B. C. and Press, S. J. (1983). Bayesian inference for Pareto populations. Journal of Econometrics, 21, 287-306. https://doi.org/10.1016/0304-4076(83)90047-7
  2. Arnold, B. C. and Press, S. J. (1989). Bayesian estimation and prediction for Pareto data. Journal of the American Statistical Association, 84, 1079-1084. https://doi.org/10.1080/01621459.1989.10478875
  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. Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of Royal Statistical Society, B, 41, 113-147.
  6. Fernandez, A. J. (2008). Highest posterior density estimation from multiply censored Pareto data. Statistical Papers, 49, 333-341.
  7. Geisser, S. (1984). Prediction Pareto and exponential observables. Canadian Journal of Statistics, 12, 143-152. https://doi.org/10.2307/3315178
  8. Geisser, S. (1985). Interval prediction for Pareto and exponential observables. Journal of Econometrics, 29, 173-185. https://doi.org/10.1016/0304-4076(85)90038-7
  9. Ghosal, S. (1997). Reference priors in multiparameter nonregular cases. Test, 6, 159-186. https://doi.org/10.1007/BF02564432
  10. Ghosal, S. (1999). Probability matching priors for non-regular cases. Biometrika, 86, 956-964. https://doi.org/10.1093/biomet/86.4.956
  11. Ghosal, S. and Samanta, T. (1997). Expansion of Bayes risk for entropy loss and reference prior in nonregular cases. Statistics and Decisions, 15, 129-140.
  12. Ghosh, J. K. and Mukerjee, R. (1992). Noninformative priors (with discussion). In Bayesian Statistics IV, edited by J. M. Bernardo et al., Oxford University Press, Oxford, 195-210.
  13. Kang, S. G. (2010). Noninformative priors for the common scale parameter in Pareto distributions. Journal of the Korean Data & Information Science Society, 21, 335-343.
  14. Kim, D. H., Kang, S. G. and Lee, W. D. (2009). Noninformative priors for Pareto distribution. Journal of the Korean Data & Information Science Society, 20, 1213-1223.
  15. Ko, J. H. and Kim, Y. H. (1999). Bayesian prediction inference for censored Pareto model. Journal of the Korean Data & Information Science Society, 10, 147-154.
  16. Lee, W. D., Kang, S. G. and Cho, J. S. (2003). On the development of probability matching priors for non-regular Pareto distribution. The Korean Communications in Statistics, 10, 333-339. https://doi.org/10.5351/CKSS.2003.10.2.333
  17. Lwin, T. (1972). Estimation of the tail of the Paretian law. Scandinavian Actuarial Journal, 55, 170-178.
  18. Nigm, A. M. and Hamdy, H. L. (1987). Bayesian prediction bounds for the Pareto lifetime model. Communications in Statistics: Theory and Methods, 16, 1761-1772. https://doi.org/10.1080/03610928708829470
  19. Soliman, A. A. (2001). LINEX and quadratic approximate Bayes estimators applied to Pareto model. Communications in Statistics: Simulation and Computation, 30, 47-62. https://doi.org/10.1081/SAC-100001857
  20. Stein, C. (1985). On the coverage probability of con dence sets based on a prior distribution. In Sequential Methods in Statistics. Banach Center Publications, 16, 485-514. https://doi.org/10.4064/-16-1-485-514
  21. Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution. In Sequential Methods in Statistics. Banach Center Publications, 16, 485-514. https://doi.org/10.4064/-16-1-485-514