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Comparison of Tests for the Equality of Several Log-Normal Means

Year 2017, Volume: 30 Issue: 3, 209 - 222, 20.09.2017

Abstract

In this paper, we
focused on testing for the equality of several log-normal means since the
log-normal distribution is one of the most common distribution for analyzing
positive and right-skewed data. Recently, many researchers proposed a lot of methods based on l
ikelihood-based methods, generalized pivotal-based methods, bootstrap-based
methods for this case. Apparently because there is not exact result related
with which test is better than others in which cases, our goal shed light on
this important problem. For this reason, we investigate these methods and
compare them with each other by simulation study.

References

  • 1] Chang, C.H. and Pal, N., “A revisit to the Behren-Fisher Problem: comparison of five test methods”, Communications in Statistics-Simulation and Computation, 37(6):1064-1085, (2008).
  • [2] Chang, C.H., Lin, J.J. and Pal, N., “Testing the equality of several gamma means: a parametric bootstrap method with applications”, Computational Statistics, 26(1):55-76, (2011).
  • [3] Crow, E.L. and Shimizu, K., Lognormal distribution, Mercel Dekker, New York, (1998).
  • [4] Gill, P.S., “Small-sample inference for the comparison of means of log-normal distributions”, Biometrics, 60(2):525–527, (2004).
  • [5] Gökpınar, F. and Gökpınar, E., "Testing the equality of several log-normal means based on a computational approach," Communications in Statistics-Simulation and Computation 46(3): 1998-2010, (2017).
  • [6] Gökpınar, E. and Gökpınar, F., “A test based on computational approach for equality of means under unequal variance assumption”, Hacettepe Journal of Mathematics and Statistics, 41(4):605-613, (2012).
  • [7] Gökpınar, E., Polat, E., Gokpinar, F. and Gunay, S., “A new computational approach for testing equality of ınverse gaussian means under heterogenity”, Hacettepe Journal of Mathematics and Statistics, 42(5):581-590, (2013).
  • [8] Gökpınar, F. and Gökpınar, E., “A Computational approach for testing of coefficients of variation in k normal population”, Hacettepe Journal of Mathematics and Statistics, 44(5):1197-1213, (2015a).
  • [9] Gökpınar, E. and Gökpınar, F., “Testing equality of variances for several normal populations”, Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2014.955110, (2015b).
  • [10] Gupta, R.C. and Li, X., “Statistical inference for the common mean of two log-normal distributions and some applications in reliability”, Computational Statistics & Data Analysis, 50:3141-3164, (2006).
  • [11] Guo, J. and Luh, W., “Testing methods for the one-way fixed effects ANOVA models of log-normal samples”, Journal of Applied Statistics, 27:731-738, (2000).
  • [12] Jafari, A.A. and Abdollahnezhad, K., "Testing the equality means of several log-normal distributions", Communications in Statistics-Simulation and Computation, 46(3): 2311-2320, (2017).
  • [13] Krishnamoorthy, K. and Mathew, T., “Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals”, Journal of Statistical Planning and Inference, 115:103-121, (2003). [14] Krishnamoorthy, K., and Oral, E., "Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean," Statistical methods in medical research, DOI:10.1177/0962280215615160, (2015).
  • [15] Lin, S.H., and Wang, R.S., "Modified method on the means for several log-normal distributions," Journal of Applied Statistics, 40(1): 194-208, (2013).
  • [16] Lin, S.H., "The higher order likelihood method for the common mean of several log-normal distributions," Metrika, 76(3): 381-392, (2013).
  • [17] Li, X., “A generalized p-value approach for comparing the means of several log-normal populations”, Statistics and Probability Letters, 79:1404-1408, (2009).
  • [18] Mutlu, H.T., Gökpınar, F., Gökpınar, E. and Gül, H.H., "A New Computational Approach Test for One-Way ANOVA under Heteroscedasticity”, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2016.117708, (2016).
  • [19] Pal, N., Lim, W. K. and Ling, C.H., “A computational approach to statistical inferences”, Journal of Applied Probability & Statistics, 2:13-35, (2007).
  • [20] Skovgaard, I. M., “Likelihood asymptotics”, Scandinavian Journal of Statistics, 28:3-32, (2001).
  • [21] Wu, J., Jiang, G., Wong, A.C.M. and Sun, X., “Likelihood analysis for the ratio of means of two independent log-normal distributions”, Biometrics, 58:463–469, (2002).
  • [22] Wu, J., Wong, A.C.M. and Jiang, G., “Likelihood-based confidence intervals for a lognormal mean”, Stat. Med., 22:1849–1860, (2003).
  • [23] Zhou, X. H., Gao, S. and Hui, S. L., “Methods for comparing the means of two independent log-normal samples”, Biometrics, 53:1129-1135, (1997).
  • [24] Zhou, X.and Tu, W., “Comparison of several independent population means when their samples contain log-normal and possibly zero observations”, Biometrics, 55:645-651, (1999).
Year 2017, Volume: 30 Issue: 3, 209 - 222, 20.09.2017

Abstract

References

  • 1] Chang, C.H. and Pal, N., “A revisit to the Behren-Fisher Problem: comparison of five test methods”, Communications in Statistics-Simulation and Computation, 37(6):1064-1085, (2008).
  • [2] Chang, C.H., Lin, J.J. and Pal, N., “Testing the equality of several gamma means: a parametric bootstrap method with applications”, Computational Statistics, 26(1):55-76, (2011).
  • [3] Crow, E.L. and Shimizu, K., Lognormal distribution, Mercel Dekker, New York, (1998).
  • [4] Gill, P.S., “Small-sample inference for the comparison of means of log-normal distributions”, Biometrics, 60(2):525–527, (2004).
  • [5] Gökpınar, F. and Gökpınar, E., "Testing the equality of several log-normal means based on a computational approach," Communications in Statistics-Simulation and Computation 46(3): 1998-2010, (2017).
  • [6] Gökpınar, E. and Gökpınar, F., “A test based on computational approach for equality of means under unequal variance assumption”, Hacettepe Journal of Mathematics and Statistics, 41(4):605-613, (2012).
  • [7] Gökpınar, E., Polat, E., Gokpinar, F. and Gunay, S., “A new computational approach for testing equality of ınverse gaussian means under heterogenity”, Hacettepe Journal of Mathematics and Statistics, 42(5):581-590, (2013).
  • [8] Gökpınar, F. and Gökpınar, E., “A Computational approach for testing of coefficients of variation in k normal population”, Hacettepe Journal of Mathematics and Statistics, 44(5):1197-1213, (2015a).
  • [9] Gökpınar, E. and Gökpınar, F., “Testing equality of variances for several normal populations”, Communications in Statistics-Simulation and Computation, DOI: 10.1080/03610918.2014.955110, (2015b).
  • [10] Gupta, R.C. and Li, X., “Statistical inference for the common mean of two log-normal distributions and some applications in reliability”, Computational Statistics & Data Analysis, 50:3141-3164, (2006).
  • [11] Guo, J. and Luh, W., “Testing methods for the one-way fixed effects ANOVA models of log-normal samples”, Journal of Applied Statistics, 27:731-738, (2000).
  • [12] Jafari, A.A. and Abdollahnezhad, K., "Testing the equality means of several log-normal distributions", Communications in Statistics-Simulation and Computation, 46(3): 2311-2320, (2017).
  • [13] Krishnamoorthy, K. and Mathew, T., “Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals”, Journal of Statistical Planning and Inference, 115:103-121, (2003). [14] Krishnamoorthy, K., and Oral, E., "Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean," Statistical methods in medical research, DOI:10.1177/0962280215615160, (2015).
  • [15] Lin, S.H., and Wang, R.S., "Modified method on the means for several log-normal distributions," Journal of Applied Statistics, 40(1): 194-208, (2013).
  • [16] Lin, S.H., "The higher order likelihood method for the common mean of several log-normal distributions," Metrika, 76(3): 381-392, (2013).
  • [17] Li, X., “A generalized p-value approach for comparing the means of several log-normal populations”, Statistics and Probability Letters, 79:1404-1408, (2009).
  • [18] Mutlu, H.T., Gökpınar, F., Gökpınar, E. and Gül, H.H., "A New Computational Approach Test for One-Way ANOVA under Heteroscedasticity”, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2016.117708, (2016).
  • [19] Pal, N., Lim, W. K. and Ling, C.H., “A computational approach to statistical inferences”, Journal of Applied Probability & Statistics, 2:13-35, (2007).
  • [20] Skovgaard, I. M., “Likelihood asymptotics”, Scandinavian Journal of Statistics, 28:3-32, (2001).
  • [21] Wu, J., Jiang, G., Wong, A.C.M. and Sun, X., “Likelihood analysis for the ratio of means of two independent log-normal distributions”, Biometrics, 58:463–469, (2002).
  • [22] Wu, J., Wong, A.C.M. and Jiang, G., “Likelihood-based confidence intervals for a lognormal mean”, Stat. Med., 22:1849–1860, (2003).
  • [23] Zhou, X. H., Gao, S. and Hui, S. L., “Methods for comparing the means of two independent log-normal samples”, Biometrics, 53:1129-1135, (1997).
  • [24] Zhou, X.and Tu, W., “Comparison of several independent population means when their samples contain log-normal and possibly zero observations”, Biometrics, 55:645-651, (1999).
There are 23 citations in total.

Details

Journal Section Statistics
Authors

Esra Gökpınar

Publication Date September 20, 2017
Published in Issue Year 2017 Volume: 30 Issue: 3

Cite

APA Gökpınar, E. (2017). Comparison of Tests for the Equality of Several Log-Normal Means. Gazi University Journal of Science, 30(3), 209-222.
AMA Gökpınar E. Comparison of Tests for the Equality of Several Log-Normal Means. Gazi University Journal of Science. September 2017;30(3):209-222.
Chicago Gökpınar, Esra. “Comparison of Tests for the Equality of Several Log-Normal Means”. Gazi University Journal of Science 30, no. 3 (September 2017): 209-22.
EndNote Gökpınar E (September 1, 2017) Comparison of Tests for the Equality of Several Log-Normal Means. Gazi University Journal of Science 30 3 209–222.
IEEE E. Gökpınar, “Comparison of Tests for the Equality of Several Log-Normal Means”, Gazi University Journal of Science, vol. 30, no. 3, pp. 209–222, 2017.
ISNAD Gökpınar, Esra. “Comparison of Tests for the Equality of Several Log-Normal Means”. Gazi University Journal of Science 30/3 (September 2017), 209-222.
JAMA Gökpınar E. Comparison of Tests for the Equality of Several Log-Normal Means. Gazi University Journal of Science. 2017;30:209–222.
MLA Gökpınar, Esra. “Comparison of Tests for the Equality of Several Log-Normal Means”. Gazi University Journal of Science, vol. 30, no. 3, 2017, pp. 209-22.
Vancouver Gökpınar E. Comparison of Tests for the Equality of Several Log-Normal Means. Gazi University Journal of Science. 2017;30(3):209-22.