Abstract
In this paper, two-sided simultaneous confidence intervals, on the lines of Hayter et al. (J Stat Plan Inference 86:81–99, 2000), to compare \(k\) two-parameter exponential populations with a control population in terms of location parameters are proposed, which combine the advantages of one-sided simultaneous confidence intervals and two-sided simultaneous confidence intervals of Bofinger (Aust J Stat 34(1):65–75, 1992). The proposed two-sided simultaneous confidence intervals also maintain the inferential sensitivity of positive directional decision of one-sided simultaneous confidence intervals. Computation of the critical constants of the proposed procedure is discussed and selected critical constants are tabulated. Working and advantages of the proposed procedure are demonstrated with a numerical example.
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References
Bofinger, E.: Comparisons and selection of two-parameter exponential populations. Aust. J. Stat. 34(1), 65–75 (1992)
Chen, H.J.: A new range statistic for comparisons of several exponential location parameters. Biometrika 69, 257–260 (1982)
Dunnett, C.W.: A multiple comparison procedure for comparing several treatments with a control. J. Am. Stat. Assoc. 50, 1096–1121 (1955)
Dunnett, C.W., Tamhane, A.C.: A step-up multiple test procedure. J. Am. Stat. Assoc. 87, 162–170 (1992)
Gail, M.H., Gastwirth, J.L.: A scale-free goodness of fit test for the exponential distribution based on the Gini Statistic. J. R. Stat. Soc. Ser. B 40, 350–357 (1978)
Hayter, A.J., Miwa, T., Liu, W.: Combining the advantages of one-sided and two-sided procedures for comparing several treatments with a control. J. Stat. Plan. Inference 86, 81–99 (2000)
Lam, K., Ng, C.K.: Two-stage procedures for comparing several exponential populations with a control when the scale parameters are unknown and unequal. Seq. Anal. 9(2), 151–164 (1990)
Levene, H.: Robust testes for equality of variances. In: Olkin, I., Hotelling, H. (eds.) Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, pp. 278–292. Stanford University Press, Stanford (1960)
Nelson, W.: Applied Life Data Analysis. Wiley, New York (1982)
Singh, P., Abebe, A.: Comparing several exponential populations with more than one control. Stat. Methods Appl. 18, 359–374 (2009)
Wu, S.F., Chen, H.J.: Multiple comparison procedures with the average for exponential location parameters. Comput. Stat. Data Anal. 26, 461–484 (1998)
Wu, S.F., Wu, C.C.: Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. J Stat. Plan. Inference 134, 392–408 (2005)
Wu, S.F., Lin, Y.P., Yu, Y.R.: One-stage multiple comparisons with the control for exponential location parameters under heteroscedasticity. Comput. Stat. Data Anal. 54(5), 1372–1380 (2010)
Zhao, H.B.: Comparing several treatments with a control. J. Stat. Plan. Inference 137, 2996–3006 (2007)
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Appendix
Appendix
# R-Code for computation of critical constant required for the implementation of “Simultaneous Confidence intervals for comparing several exponential location parameters with control”
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Singh, P., Goyal, A. & Gill, A.N. Simultaneous confidence intervals for comparing several exponential location parameters with a control. METRON 73, 99–118 (2015). https://doi.org/10.1007/s40300-014-0054-z
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DOI: https://doi.org/10.1007/s40300-014-0054-z