IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i1d10.1007_s11009-018-9639-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9639-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-018-9639-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Stephanie Aerts & Gentiane Haesbroeck, 2017. "Robust asymptotic tests for the equality of multivariate coefficients of variation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 163-187, March.
    3. Yongku Kim & Woo Dong Lee & Sang Gil Kang, 2020. "A matching prior based on the modified profile likelihood for the common mean in multiple log-normal distributions," Statistical Papers, Springer, vol. 61(2), pages 543-573, April.
    4. S. Lin, 2013. "The higher order likelihood method for the common mean of several log-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 381-392, April.
    5. 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.
    6. Al-Mutairi, D.K. & Ghitany, M.E. & Gupta, Ramesh C., 2011. "Estimation of reliability in a series system with random sample size," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 964-972, February.
    7. Zhou, Jianhui, 2009. "Robust dimension reduction based on canonical correlation," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 195-209, January.
    8. Graciela Boente & Frank Critchley & Liliana Orellana, 2007. "Influence functions of two families of robust estimators under proportional scatter matrices," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 295-327, February.
    9. Bianco, Ana & Boente, Graciela & Pires, Ana M. & Rodrigues, Isabel M., 2008. "Robust discrimination under a hierarchy on the scatter matrices," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1332-1357, July.
    10. Ayanendranath Basu & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2018. "Robust Wald-type tests for non-homogeneous observations based on the minimum density power divergence estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 493-522, July.
    11. Chang, Ming & You, Xuqun & Wen, Muqing, 2012. "Testing the homogeneity of inverse Gaussian scale-like parameters," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1755-1760.
    12. A. García-Pérez, 2012. "A linear approximation to the power function of a test," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 855-875, October.
    13. Boente, Graciela & Molina, Julieta & Sued, Mariela, 2010. "On the asymptotic behavior of general projection-pursuit estimators under the common principal components model," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 228-235, February.
    14. Abhijit Mandal & Beste Hamiye Beyaztas & Soutir Bandyopadhyay, 2023. "Robust density power divergence estimates for panel data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 773-798, October.
    15. Alfonso García-Pérez, 2023. "A New Estimator: Median of the Distribution of the Mean in Robustness," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    16. Elżbieta Szaruga & Elżbieta Załoga, 2022. "Qualitative–Quantitative Warning Modeling of Energy Consumption Processes in Inland Waterway Freight Transport on River Sections for Environmental Management," Energies, MDPI, vol. 15(13), pages 1-21, June.
    17. 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.
    18. Ali Akbar Jafari & Javad Shaabani, 2020. "Comparing scale parameters in several gamma distributions with known shapes," Computational Statistics, Springer, vol. 35(4), pages 1927-1950, December.
    19. Prendergast, Luke A. & Smith, Jodie A., 2022. "Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    20. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9639-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.