Simultaneous Fiducial Generalized Confidence Intervals for Ratios of Means of Lognormal Distributions

Authors

  • Jan Hannig Colorado State University, U.S.A.
  • Lidong E Colorado State University, U.S.A.
  • Amany Abdel-Karim Colorado State University, U.S.A.
  • Hari Iyer Colorado State University, U.S.A.

DOI:

https://doi.org/10.17713/ajs.v35i2&3.372

Abstract

In this paper, we construct Fiducial Generalized Confidence Intervals (FGCI) for ratio of means of two lognormal distributions based on independent observations from the two distributions. We compared the proposed method with another method, the Z-Score method. A simulation study showed that the FGCI method performs much better than the Z-Score method, especially for small and medium samples. We also prove that the confidence intervals constructed using FGCI method have correct asymptotic coverage.
In this paper we propose a new method for constructing simultaneous confidence intervals for all pairwise ratios of means of lognormal distributions. Our approach is based on Fiducial Generalized Pivotal Quantities (FGPQ) for vector parameters. Simulation studies show that the constructed confidence intervals have satisfactory small sample performance. We also prove that they have correct asymptotic coverage. The result has applications in
bioequivalence studies for comparing three or more drug formulations.

References

Abdel-Karim, A. (2005). Applications of Generalized Inference. Unpublished doctoral dissertation, Colorado State University, Fort Collins, Colorado.

Behrens, W.-V. (1929). Ein Beitrag zur Fehlerberchnung bei wenigen Beobachtungen. Landwirtschaftliches Jahrbuch, LXVIII, 807-837.

Billingsley, P. (1995). Probability and Measure (3rd ed.). New York: J. Wiley.

Fisher, R. A. (1935). The fiducial argument in statistical inference. Annals of Eugenics, VI, 91-98.

Fisher, R. A. (1939). Samples with possibly unequal variances. Annals of Eugenics, IX, 174-180.

Hannig, J. (2005). On multidimensional fiducial generalized confidence intervals (Tech. Rep. No. 2005/1). Colorado State University.

Hannig, J., Iyer, H. K., and Patterson, P. L. (2005). Fiducial generalized confidence intervals. Journal of the American Statistical Association, to appear.

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

Lidong, E., Hannig, J., and Iyer, H. K. (2005). Fiducial Generalized Confidence Intervals for Functions of Lognormal Means and Variances (Tech. Rep.). Colorado State University, Fort Collins, Colorado.

Tsui, K. W., and Weerahandi, S. (1989). Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. Journal of the American Statistical Association, 84(406), 602-607.

U.S. Food and Drug Administration. (2001). Guidance to industry - statistical approaches to establishing bioequivalence. U.S. Department of Health and Human Services, Food and Drug Administration.

Weerahandi, S. (1993). Generalized confidence intervals. Journal of the American Statistical Association, 88(423), 899-905.

Zhou, X. H., Gao, S., and Hui, S. L. (1997). Methods for comparing the means of two independent log-normal samples. Biometrics, 53(3), 1129-1135.

Downloads

Published

2016-04-03

How to Cite

Hannig, J., E, L., Abdel-Karim, A., & Iyer, H. (2016). Simultaneous Fiducial Generalized Confidence Intervals for Ratios of Means of Lognormal Distributions. Austrian Journal of Statistics, 35(2&3), 261–269. https://doi.org/10.17713/ajs.v35i2&3.372

Issue

Vol. 35 No. 2&3 (2006)

Section

Articles

License

The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. 

The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.

Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.

 

Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.