Non informative priors for common shape parameter in the Pareto distributions
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we develop the noninformative priors for the common shape parameter in the Pareto distributions. We develop the matching pri-ors and the reference priors. It turns out that the second order matching prior does not exist. Also we reveal that the one-at-a-time reference prior satisfies the first order matching criterion. Through simulation study,we show that the proposed reference prior matches the target coverage probabilities in a frequentist sense.
Abstract
In this paper, we develop the noninformative priors for the common shape parameter in the Pareto distributions. We develop the matching pri-ors and the reference priors. It turns out that the second order matching prior does not exist. Also we reveal that the one-at-a-time reference prior satisfies the first order matching criterion. Through simulation study,we show that the proposed reference prior matches the target coverage probabilities in a frequentist sense.
참고문헌 (30)
- Arnold, B.C, "Bayesian inference for Pareto popu- lations", Journal of Econometrics, 21, pp.287~306 (1983)
- Arnold, B.C, "Bayesian estimation and prediction for Pareto data", Journal of the American Statistical Association, 84, pp.1079~1084 (1989)
- Berger, J.O, "Estimating a Product of Means: Bayesian analysis with reference priors", Journal of the American Statis-tical Association, 84, pp.200~207 (1989)
- Berger, J.O, "On the development of reference priors (with discussion), In Bayesian Statistics IV", pp.35~60 (1992), Oxford University Press
- Bernardo, J.M, "Reference posterior distributions for Bayesian inference (with discussion)", Journal of Royal Statistical Society B, 41, pp.113~147 (1979)
- Cox, D.R, "Orthogonal parameters and approximate conditional inference (with discussion)", Journal of Royal Statistical Soci- ety B, 49, pp.1~39 (1987)
- Datta, G.S, "On priors providing frequentist validity for Bayesian inference", Biometrika, 82, pp.37~45 (1995)
- Datta, G.S, "Some remarks on noninformative priors", Journal of the American Statistical Association, 90, pp.1357~1363 (1995)
- Datta, G.S, "On the invariance of noninformative priors", The Annal of Statistics, 24, pp.141~159 (1996)
- DiCiccio, T.J, "Frequentist and Bayesian Bartlett correction of test statistics based on adjusted prole likelihood", Journal of Royal Statistical Society B, 56, pp.397~408 (1994)
- Fernandez, A.J, "Highest posterior density estimation form multi- ply censored Pareto data", Statistical Papers, 49, pp.333~341 (2008)
- Geisser, S, "Prediction Pareto and exponential observables", Cana- dian Journal of Statistics, 12, pp.143~152 (1984)
- Geisser, S., "Interval prediction for Pareto and exponential observ- ables", Journal of Econometrics, 29, pp.173~185 (1985)
- Ghosh, J.K, "Noninformative priors (with dis- cussion), In Bayesian Statistics IV", pp.195~210 (1992), Oxford University Press
- 강상길, "Noninformative priors for the common scale parameter in Pareto distributions", 한국데이터정보과학회지, 21(2), pp.335~343 (2010), 한국데이터정보과학회
- 강상길, "Noninformative Priors for the Common Shape Parameter in the Gamma Distributions", 한국데이터정보과학회지, 18(1), pp.247~257 (2007), 한국데이터정보과학회
- 김달호, "Noninformative priors for Pareto distribution", 한국데이터정보과학회지, 20(6), pp.1213~1223 (2009), 한국데이터정보과학회
- Ko, J.H, "Bayesian prediction inference for censored Pareto model", Journal of the Korean Data & Information Science Society, 10, pp.147~154 (1999)
- Lwin, T, "Estimation of the tail of the Paretian law", Scandinavian Actuarial Journal, 55, pp.170~178 (1972)
- Mukerjee, R, "Frequentist validity of posterior quan-tiles in the presence of a nuisance parameter : higher order asymptotics", Biometrika, 80, pp.499~505 (1993)
- Mukerjee, R, "Second order probability matching priors", Biometrika, 84, pp.970~975 (1997)
- Nelson, W.B., "Graphical analysis of accelerated life test data with the inverse power law model", IEEE Transactions on Reliability, 21, pp.2~11 (1972)
- Nigm, A.M, "Bayesian prediction bounds for the Pareto lifetime model", Communications in Statistics: Theory and Methods, 16, pp.1761~1772 (1987)
- Stein, C, "On the coverage probability of condence sets based on a prior distribution", Sequential Methods in Statistics, Banach Center Publications, 16, pp.485~514 (1985)
- Stone, G.C., "Application of Weibull statistics to insulation aging tests", IEEE Transactions on Electrical and Insulation, 14, pp.233~239 (1979)
- Tibshirani, R, "Noninformative priors for one parameter of many", Biometrika, 76, pp.604~608 (1989)
- Tiwari, R.C, "Bayes estimation for the Pareto failure-model using gibbs sampling", IEEE Transactions on Reliability, 45, pp.471~476 (1996)
- Welch, B.L., "On formulae for condence points based on integrals of weighted likelihood", Journal of Royal Statistical Society B, 25, pp.318~329 (1963)
- Wong, A.C.M, "Comparisons of approximate tail prob- abilities for the shape parameter of the Gamma distribution", Computa-tional Statistics & Data Analysis, 27, pp.333~344 (1998)
- Yang Z, "Improved maximum-likelihood estimation for the common shape parameter of several Weibull populations", Applied Stochastic Models in Business and Industry, 23, pp.373~383 (2007)
