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One-stage multiple comparisons with the control for exponential location parameters under heteroscedasticity

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  • Wu, Shu-Fei
  • Lin, Ying-Po
  • Yu, Yuh-Ru

Abstract

Two-stage multiple comparisons with the control for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Lam and Ng [Lam, K., Ng, C.K., 1990. Two-stage procedures for comparing several exponential populations with a control when the scale parameters are unknown and unequal. Sequential Analysis 9 (2) 151-164]. When the additional sample for the second stage may not be available, one-stage procedures including one-sided and two-sided confidence intervals are proposed in this paper. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, medical research, and automodels. Tables of upper limits of critical values are obtained using the technique given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection, Sydney, Australia, August 1987; Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics -- Simulation and Computation 17 (3) 995-1006]. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. The relationship between the one-stage and the two-stage procedure is also discussed in this paper.

Suggested Citation

  • Wu, Shu-Fei & Lin, Ying-Po & Yu, Yuh-Ru, 2010. "One-stage multiple comparisons with the control for exponential location parameters under heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1372-1380, May.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1372-1380
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    Cited by:

    1. Maurya, Vishal & Gill, A.N. & Goyal, Aarti, 2017. "A new two-stage multiple comparison procedure for comparing several exponential populations with a control under heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 1-11.
    2. Parminder Singh & Anju Goyal & Amar Gill, 2015. "Simultaneous confidence intervals for comparing several exponential location parameters with a control," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 99-118, April.
    3. A. Malekzadeh & M. Kharrati-Kopaei & S. Sadooghi-Alvandi, 2014. "Comparing exponential location parameters with several controls under heteroscedasticity," Computational Statistics, Springer, vol. 29(5), pages 1083-1094, October.
    4. Vishal Maurya & Amar Nath Gill & Parminder Singh, 2013. "Multiple comparisons with a control for exponential location parameters under heteroscedasticity," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1817-1830, August.
    5. Kharrati-Kopaei, Mahmood & Malekzadeh, Ahad & Sadooghi-Alvandi, Mohammad, 2013. "Simultaneous fiducial generalized confidence intervals for the successive differences of exponential location parameters under heteroscedasticity," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1547-1552.
    6. Shu-Fei Wu, 2022. "Multiple Comparison Procedures for Exponential Mean Lifetimes Compared with Several Controls," Mathematics, MDPI, vol. 10(4), pages 1-10, February.

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