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A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples

Author

Listed:
  • Ayanendranath Basu

    (Indian Statistical Institute)

  • Abhijit Mandal

    (Wayne State University)

  • Nirian Martín

    (Complutense University of Madrid)

  • Leandro Pardo

    (Complutense University of Madrid)

Abstract

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis for comparing the means of two independent log-normal distributions is an issue of significant interest. In this paper we present a robust test for this problem. The unknown parameters of the model are estimated by minimum density power divergence estimators (Basu et al. Biometrika 85(3):549–559 1998). The robustness as well as the asymptotic properties of the proposed test statistics are rigorously established. The performance of the test is explored through simulations and real data analysis. The test is compared with some existing methods, and it is demonstrated that the proposed test outperforms the others in the presence of outliers.

Suggested Citation

  • Ayanendranath Basu & Abhijit Mandal & Nirian Martín & Leandro Pardo, 2019. "A Robust Wald-Type Test for Testing the Equality of Two Means from Log-Normal Samples," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 85-107, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9639-y
    DOI: 10.1007/s11009-018-9639-y
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    References listed on IDEAS

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    1. Gupta, Ramesh C. & Li, Xue, 2006. "Statistical inference for the common mean of two log-normal distributions and some applications in reliability," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3141-3164, July.
    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. Ghosh, Abhik & Mandal, Abhijit & Martín, Nirian & Pardo, Leandro, 2016. "Influence analysis of robust Wald-type tests," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 102-126.
    4. Jiin-Huarng Guo & Wei-Ming Luh, 2000. "Testing methods for the one-way fixed effects ANOVA models of log-normal samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 731-738.
    5. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
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