A revisit to testing the equality of means for several lognormal distributions

References

• Limpert E, Stahel WA, Abbt M. Log-normal distributions across the sciences: keys and clues. BioScience 2001;51(5):341–352. doi: 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2
   Web of Science ®Google Scholar
• Bishop PG, Bloomfield RE. Using a log-normal failure rate distribution for worst case bound reliability prediction. In: 14th International Symposium on Software Reliability Engineering. ISSRE 2003. Denver, IEEE; Nov 2003. p. 237–245.
   Google Scholar
• Alhadeed AA, Yang SS. Optimal simple step-stress plan for cumulative exposure model using log-normal distribution. IEEE Trans Reliab. 2005;54(1):64–68. doi: 10.1109/TR.2004.841704
   Web of Science ®Google Scholar
• Boributh S, Jiraratananon R, Li K. Analytical solutions for membrane wetting calculations based on log-normal and normal distribution functions for CO2 absorption by a hollow fiber membrane contactor. J Memb Sci. 2013;429:459–472. doi: 10.1016/j.memsci.2012.11.074
   Web of Science ®Google Scholar
• Cheng M, Chen C, Gao J, et al. Capacity of wander and spread beams in log-normal distribution non-Kolmogorov turbulence optical links. Optik. 2014;125(14):3714–3717. doi: 10.1016/j.ijleo.2014.01.127
   Web of Science ®Google Scholar
• Monteiro MJ. Fitting molecular weight distributions using a log-normal distribution model. Eur Polym J. 2015;65:197–201. doi: 10.1016/j.eurpolymj.2015.01.009
   Web of Science ®Google Scholar
• Lubrano M, Ndoye AAJ. Income inequality decomposition using a finite mixture of log-normal distributions: a Bayesian approach. Comput Stat Data Anal. 2016;100:830–846. doi: 10.1016/j.csda.2014.10.009
   Web of Science ®Google Scholar
• Bølviken E, Guillen M. Risk aggregation in Solvency II through recursive lognormals. Insur Math Econ. 2017;73:20–26. doi: 10.1016/j.insmatheco.2016.12.006
   Web of Science ®Google Scholar
• Zhou XH, Gao S, Hui SL. Methods for comparing the means of two independent log-normal samples. Biometrics. 1997;53:1129–1135. doi: 10.2307/2533570
   PubMed Web of Science ®Google Scholar
• Li X. A generalized p-value approach for comparing the means of several lognormal populations. Stat Probab Lett. 2009;79(11):1404–1408. doi: 10.1016/j.spl.2009.03.004
   Web of Science ®Google Scholar
• Lin S, Wang R. Modified method on the means for several log-normal distributions. J Appl Stat. 2013;40(1):194–208. doi: 10.1080/02664763.2012.740622
   Web of Science ®Google Scholar
• Krishnamoorthy K, Oral E. Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean. Stat Methods Med Res. 2017;26(6):2919–2937. doi: 10.1177/0962280215615160
   PubMed Web of Science ®Google Scholar
• Gokpinar F, Gokpinar E. Testing the equality of several log-normal means based on a computational approach. Commun Stat Simul Comput. 2017;46(3):1998–2010. doi: 10.1080/03610918.2015.1030413
   Web of Science ®Google Scholar
• Jafari AA, Abdollahnezhad K. Testing the equality means of several log-normal distributions. Commun Stat Simul Comput. 2017; 46(3):2311–2320. doi: 10.1080/03610918.2015.1041976
   Web of Science ®Google Scholar
• Zhou X-H, Tu W. Comparison of several independent population means when their samples contain log-normal and possibly zero observations. Biometrics. 1999;55(2):645–651. doi: 10.1111/j.0006-341X.1999.00645.x
   PubMed Web of Science ®Google Scholar
• Wu J, Jiang G, Wong A, et al. Likelihood analysis for the ratio of means of two independent log-normal distributions. Biometrics. 2002;58(2):463–469. doi: 10.1111/j.0006-341X.2002.00463.x
   PubMed Web of Science ®Google Scholar
• Lin SH. The higher order likelihood method for the common mean of several lognormal distributions. Metrika. 2013;76(3):381–392. doi: 10.1007/s00184-012-0393-9
   Web of Science ®Google Scholar
• Krishnamoorthy K, Mathew T. Inferences on the means of lognormal distributions using generalized p-values and generalized confidence intervals. J Stat Plan Inference. 2003;115(1):103–121. doi: 10.1016/S0378-3758(02)00153-2
   Web of Science ®Google Scholar
• Pal N, Lim WK, Ling CH. A computational approach to statistical inferences. J Appl Probab Stat. 2007;2(1):13–35.
   Google Scholar
• Chang CH, Pal N. A revisit to the Behrens–Fisher problem: comparison of five test methods. Commun Stat Simul Comput. 2008;37(6):1064–1085. doi: 10.1080/03610910802049599
   Web of Science ®Google Scholar
• Chang CH, Pal N, Lim WK, et al. Comparing several population means: a parametric bootstrap method, and its comparison with usual ANOVA F test as well as ANOM. Comput Stat. 2010;25(1):71–95. doi: 10.1007/s00180-009-0162-z
   Web of Science ®Google Scholar
• Chang CH, Pal N, Lin JJ. A note on comparing several Poisson means. Commun Stat Simul Comput. 2010;39(8):1605– 1627. doi: 10.1080/03610918.2010.508860
   Web of Science ®Google Scholar
• Chang CH, Lin JJ, Pal N. Testing the equality of several Gamma means: A parametric bootstrap method with applications. Comput Stat. 2011;26(1):55–76. doi: 10.1007/s00180-010-0209-1
   Web of Science ®Google Scholar
• Gökpınar EY, Gökpınar F. A test based on the computational approach for equality of means under the unequal variance assumption. Hacet J Math Stat. 2012;41(4):605–613.
   Web of Science ®Google Scholar
• Gökpınar EY, Polat E, Gokpınar F, et al. A new computational approach for testing equality of inverse Gaussian means under heterogeneity. Hacet J Math Stat. 2013;42(5):581–590.
   Web of Science ®Google Scholar
• Davison AC, Hinkley DV. Bootstrap methods and their application. Cambridge: Cambridge University Press; 1997.
   Google Scholar
• Engle RF. Wald, likelihood ratio, and Lagrange multiplier tests in econometrics. In: Griliches Z, Intriligator MD, editors. Handbook of Econometrics, vol 2. Amsterdam: Elsevier; 1984. p. 775–826.
   Google Scholar
• Cameron E, Pauling L. Supplemental ascorbate in the supportive treatment of cancer: re-evaluation of prolongation of survival times in terminal human cancer. Proc Natl Acad Sci USA. 1978;75(9):4538–4542. doi: 10.1073/pnas.75.9.4538
   PubMed Web of Science ®Google Scholar
• Hand DJ, Daly F, McConway K, et al. A handbook of small data sets, vol. 1. New York: Chapman and Hall/CRC Press; 1993.
   Google Scholar
• Tuncay A. Parameter estimation and test statistics in survival analysis and an application [Master’s thesis]. Samsun: Ondokuz Mayıs University; 2005.
   Google Scholar