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Noninformative priors for the common scale parameter in Pareto distributions  

Kang, Sang-Gil (Department of Computer and Data Information, Sangji University)
Publication Information
Journal of the Korean Data and Information Science Society / v.21, no.2, 2010 , pp. 335-343 More about this Journal
Abstract
In this paper, we develop the reference priors for the common scale parameter in the nonregular Pareto distributions with unequal shape paramters. We derive the reference priors as noninformative prior and prove the propriety of joint posterior distribution under the general prior including the reference priors. Through the simulation study, we show that the proposed reference priors match the target coverage probabilities in a frequentist sense.
Keywords
Nonregular case; pareto distribution; reference prior; scale parameter;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 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.   DOI   ScienceOn
2 Lee J. and Lee, W. D. (2008). Likelihood based inference for the shape parameter of Pareto distribution. Journal of the Korean Data & Information Science Society, 19, 1173-1181.   과학기술학회마을
3 Lwin, T. (1972). Estimation of the tail of the Paretian law. Scandinavian Actuarial Journal, 55, 170-178.
4 Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors. Biometrika, 84, 970-975.   DOI   ScienceOn
5 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.
6 Ghosh, J. K. and Mukerjee, R. (1992). Noninformative priors (with discussion). Bayesian Statistics IV, J.M. Bernardo, et al., Oxford University Press, Oxford, 195-210.
7 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.   과학기술학회마을
8 Fernandez, A. J. (2008). Highest posterior density estimation from multiply censored Pareto data. Statistical Papers, 49, 333-341.
9 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.
10 Elfessi, A. and Jin, C. (1996). On robust estimation of the common scale parameter of several Pareto distributions. Statistics & Probability Letters, 29, 345-352.   DOI   ScienceOn
11 Geisser, S. (1984). Prediction Pareto and exponential observables. Canadian Journal of Statistics, 12, 143-152.   DOI
12 Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of Royal Statistical Society, B, 113-147.
13 Geisser, S. (1985). Interval prediction for Pareto and exponential observables. Journal of Econometrics, 29, 173-185.   DOI   ScienceOn
14 Ghosal, S. (1997). Reference priors in multiparameter nonregular cases. Test, 6, 159-186.   DOI
15 Ghosal, S. (1999). Probability matching priors for non-regular cases. Biometrika, 86, 956-964.   DOI   ScienceOn
16 Datta, G. S. (1996). On priors providing frequentist validity for Bayesian inference for multiple parametric functions. Biometrika, 83, 287-298.   DOI   ScienceOn
17 Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors (with discussion). Bayesian Statistics IV, J.M. Bernardo, et al., Oxford University Press, Oxford, 35-60.
18 Datta, G. S. and Ghosh, J. K. (1995). On priors providing frequentist validity for Bayesian inference. Biometrika, 82, 37-45.   DOI
19 DiCiccio, T. J. and Stern, S. E. (1994). Frequentist and Bayesian Bartlett correction of test statistics based on adjusted profile likelihood. Journal of Royal Statistical Society, B, 56, 397-408.
20 Arnold, B. C. and Press, S. J. (1989). Bayesian estimation and prediction for Pareto data. Journal of the American Statistical Association, 84, 1079-1084.   DOI   ScienceOn
21 Tibshirani, R. (1989). Noninformative priors for one parameter of many. Biometrika, 76, 604-608.   DOI   ScienceOn
22 Arnold, B. C. and Press, S. J. (1983). Bayesian inference for Pareto populations. Journal of Econometrics, 21, 287-306.   DOI   ScienceOn
23 Tiwari, R. C., Yang, Y. and Zalkikar, J. N. (1996). Bayes estimation for the Pareto failure-model using Gibbs sampling. IEEE Transactions on Reliability, 45, 471-476.   DOI   ScienceOn
24 Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihood. Journal of Royal Statistical Society, B, 318-329.
25 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.   DOI   ScienceOn
26 Stein, C. (1985). On the coverage probability of confidence sets based on a prior distribution. Sequential Methods in Statistics. Banach Center Publications, 16, 485-514.