JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Noninformative priors for linear function of parameters in the lognormal distribution
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Noninformative priors for linear function of parameters in the lognormal distribution
Lee, Woo Dong; Kim, Dal Ho; Kang, Sang Gil;
  PDF(new window)
 Abstract
This paper considers the noninformative priors for the linear function of parameters in the lognormal distribution. The lognormal distribution is applied in the various areas, such as occupational health research, environmental science, monetary units, etc. The linear function of parameters in the lognormal distribution includes the expectation, median and mode of the lognormal distribution. Thus we derive the probability matching priors and the reference priors for the linear function of parameters. Then we reveal that the derived reference priors do not satisfy a first order matching criterion. Under the general priors including the derived noninformative priors, we check the proper condition of the posterior distribution. Some numerical study under the developed priors is performed and real examples are illustrated.
 Keywords
Linear function of parameters;lognormal distribution;matching prior;reference prior;
 Language
English
 Cited by
 References
1.
Angus, J. E. (1994). Bootstrap one-sided confidence intervals for the log-normal mean. Statistician, 43, 395-401. crossref(new window)

2.
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. crossref(new window)

3.
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.

4.
Bernardo, J.M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of Royal Statistical Society B, 41, 113-147.

5.
Cameron, E. and Pauling, L. (1978). Supplemental ascorbate in the supportive treatment of cancer: Reevaluation of prolongation of survival times in terminal human cancer. Proceedings of the National Academy of Science USA, 75, 4538-4532. crossref(new window)

6.
Datta, G. S. and Ghosh, M. (1995). Some remarks on noninformative priors. Journal of the American Statistical Association, 90, 1357-1363. crossref(new window)

7.
Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors. The Annals of Statistics, 24, 141-159. crossref(new window)

8.
Ghosh, J. K. and Mukerjee, R. (1992). Noninformative 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, Oxford, 195-210.

9.
Kang, S. G. (2013). Noninformative priors for the scale parameter in the generalized Pareto distribution. Journal of the Korean Data & Information Science Society, 24, 1521-1529. crossref(new window)

10.
Kang, S. G., Kim, D. H. and Lee, W. D. (2013). Noninformative priors for the ratio of parameters of two Maxwell distributions. Journal of the Korean Data & Information Science Society, 24, 643-650. crossref(new window)

11.
Kang, S. G., Kim, D. H. and Lee, W. D. (2014). Noninformative priors for the log-logistic distribution. Journal of the Korean Data & Information Science Society, 25, 227-235. crossref(new window)

12.
Krishnamoorthy, K. and Mathew, T. (2003). Inferences on the means of lognormal distributions using generalized p-values and generalized condence intervals. Journal of Statistical Planning and Inference, 115, 103-121. crossref(new window)

13.
Land, C. E. (1972). An evaluation of approximate condence interval estimation methods for lognormal means. Technometrics, 14, 145-158. crossref(new window)

14.
Lee, E. T. (1992). Statistical methods for survival data analysis, 2nd Ed., Wiley, New York.

15.
Limpert, E., Stahel, W. A. and Abbt, M. (2001). Log-normal distributions across the science: Keys and clues. BioScience, 51, 341-352. crossref(new window)

16.
Longford, N. T. and Pittau, M. G. (2006). Stability of household income in European countries in the 1990s. Computational Statistics and Data Analysis, 51, 1364-1383. crossref(new window)

17.
Mukerjee, R. and Dey, D. K. (1993). Frequentist validity of posterior quantiles in the presence of a nuisance parameter : Higher order asymptotics. Biometrika, 80, 499-505. crossref(new window)

18.
Mukerjee, R. and Ghosh, M. (1997). Second order probability matching priors. Biometrika, 84, 970-975. Journal of the American Statistical Association, 59, 665-680. crossref(new window)

19.
Parkhurst, D. F. (1998). Arithmetic versus geometric means for environmental concentration data. Environmental Science & Technology, 88, 92A-98A.

20.
Rappaport, S. M. and Selvin, S. (1987). A method for evaluating the mean exposure from a lognormal distribution. American Industrial Hygiene Journal, 48, 374-379. crossref(new window)

21.
Stein, C. (1985). On the coverage probability of condence sets based on a prior distribution. Sequential Methods in Statistics, Banach Center Publications, 16, 485-514.

22.
Tibshirani, R. (1989). Noninformative priors for one parameter of many. Biometrika, 76, 604-608. crossref(new window)

23.
Welch, B. L. and Peers, H. W. (1963). On formulae for condence points based on integrals of weighted likelihood. Journal of Royal Statistical Society B, 25, 318-329.

24.
Wu, J., Wong, A. C. M. and Jiang, G. (2003). Likelihood-based intervals for a log-normal mean. Statistics in Medicine, 22, 1849-1860. crossref(new window)

25.
Zabel, J. (1999). Controlling for quality in house price indices. The Journal of Real Estate Finance and Economics, 13, 223-241.

26.
Zhou, X. H. and Gao, S. (1997). Condence intervals for the log-normal mean. Statistics in Medicine, 16, 783-790. crossref(new window)