A note on the multiple comparisons of exponential location parameters with several controls under heteroscedasticity

Year 2018, Volume: 47 Issue: 2, 447 - 461, 01.04.2018

Mahmood Kharrati-kopaei Ehsan Kharati Koopaei

Abstract

Several researchers have addressed the problem of constructing simultaneous confidence intervals (SCIs) for comparing exponential location parameters with a control or controls under heteroscedasticity when sample sizes are equal or unequal. They usually used simulation-based inference procedures or Lam's technique that leads to conservative SCIs. In this paper, we present a set of SCIs for comparing exponential location parameters with a control, controls and the best control under heteroscedasticity when sample sizes are possibly unequal. Our method is not a simulation-based inference procedure and our results show that the proposed SCIs have some advantages over others.

Keywords

Average volume, Coverage probability, Conservative, Simulation

References

• Chang, Y. P., Huang, W. T. Simultaneous ducial generalized condence intervals for all pairwise comparisons of means, International Journal of information and Management Sci- ences 20, 459-467, 2009.
• Hannig, J., Iyer, H., Patterson, P. Fiducial generalized condence intervals, Journal of American Statistical Association 101, 254-269, 2006a.
• Hannig, J., Lidong, E., Abdel-Karim, A., Iyer, H. Simultaneous ducial generalized con- dence intervals for ratios of means of Lognormal distributions, Austrian Journal of Statis- tics, 35, 261-269, 2006b.
• Kharrati-Kopaei, M. A note on the simultaneous condence intervals for the successive dierences of exponential location parameters under heteroscedasticity, Statistical Method- ology 22, 1-7, 2015.
• Kharrati-Kopaei, M., Malekzadeh, A., Sadooghi-Alvandi, S. M. Simultaneous ducial gener- alized condence intervals for the successive dierences of exponential location parameters under heteroscedasticity, Statistics and Probability Letters 83, 1547-1552, 2013.
• Lam, K. Subset selection of normal population under heteroscedasticity, in: Proceedings of the second international advanced seminar/workshop on inference procedures associated with statistical ranking and selection, Sydney, Australia, 1987.
• Lam, K. An improved two-stage selection procedure, Communications in Statistics, Simu- lation and Computation 17 (3), 995-1005, 1988.
• Lam, K., Ng, C. K. Two-stage procedures for comparing several exponential populations with a control when scale parameters are unknown and unequal, Sequential Analysis 9 (2), 151-164, 1990.
• Lawless, J. F., Singhal, K. Analysis of data from life test experiments under an exponential model, Naval Research Logistic Quarterly 27, 323-334, 1980.
• Malekzadeh, A., Kharrati-Kopaei, M., Sadooghi-Alvandi, S. M. Comparing Exponential Location Parameters with Several Controls Under Heteroscedasticity, Computational Sta- tistics, DOI 10.1007/s00180-014-0481-6, 2014.
• Maurya, V., Gill, A. N., Singh, P. Multiple comparisons with a control for exponential location parameters under heteroscedasticity, Journal of Applied Statistics 40, 1817-1830, 2013.
• Maurya, V., Goyal, A., Gill, A. N. Multiple comparisons with more than one control for exponential location parameters under heteroscedasticity, Communications in Statistics- Simulation and Computation 40, 621-644, 2011.
• Ng, C. K., Lam, K., Chen, H. J. Multiple comparisons of exponential location parameters with the best under type II censoring, American Journal of Mathematical and Management Sciences 12, 383-402, 1993.
• Singh, P., Abebe, A. Comparing several exponential populations with more than one control, Statistical Methods and Applications 18, 359-374, 2009.
• Wu, S., Lin, Y. P., Yu, Y. R. One-stage multiple comparisons with the control for exponential location parameters under heteroscedasticity, Computational Statistics and Data Analysis 54, 1372-1380, 2010.
• Wu, S. F., Wu C. C. Two-stage multiple comparisons with the average for exponential location parameters under heteroscedasticity, Journal of Statistics and Planning Inference 134, 392-408, 2005.
• Zelen, M. Application of exponential models problems in cancer research, Journal of Royal Statistical Society Series A (129), 368-398, 1966.