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Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach

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  • Sadooghi-Alvandi, S.M.
  • Malekzadeh, A.

Abstract

For constructing simultaneous confidence intervals for the ratios of means of several lognormal distributions, we propose a new parametric bootstrap method, which is different from an inaccurate parametric bootstrap method previously considered in the literature. Our proposed method is conceptually simpler than other proposed methods, which are based on the concepts of generalized pivotal quantities and fiducial generalized pivotal quantities. Also, our extensive simulation results indicate that our proposed method consistently performs better than other methods: its coverage probability is close to the nominal confidence level and the resulting intervals are typically shorter than the intervals produced by other methods.

Suggested Citation

  • Sadooghi-Alvandi, S.M. & Malekzadeh, A., 2014. "Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 133-140.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:133-140
    DOI: 10.1016/j.csda.2013.07.039
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    References listed on IDEAS

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    1. Li, Xinmin & Wang, Juan & Liang, Hua, 2011. "Comparison of several means: A fiducial based approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1993-2002, May.
    2. Li, Xinmin, 2009. "A generalized p-value approach for comparing the means of several log-normal populations," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1404-1408, June.
    3. Xu, Li-Wen & Yang, Fang-Qin & Abula, Aji’erguli & Qin, Shuang, 2013. "A parametric bootstrap approach for two-way ANOVA in presence of possible interactions with unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 172-180.
    4. Schaarschmidt, Frank, 2013. "Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 265-275.
    5. Krishnamoorthy, K. & Lu, Fei & Mathew, Thomas, 2007. "A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5731-5742, August.
    6. Hannig, Jan & Iyer, Hari & Patterson, Paul, 2006. "Fiducial Generalized Confidence Intervals," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 254-269, March.
    7. Zhou, Xiao-Hua & Tu, Wanzhu, 2000. "Interval estimation for the ratio in means of log-normally distributed medical costs with zero values," Computational Statistics & Data Analysis, Elsevier, vol. 35(2), pages 201-210, December.
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    Cited by:

    1. Weizhong Tian & Yaoting Yang & Tingting Tong, 2022. "Confidence Intervals Based on the Difference of Medians for Independent Log-Normal Distributions," Mathematics, MDPI, vol. 10(16), pages 1-14, August.

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