Simultaneous confidence intervals for all differences of coefficients of variation of log-normal distributions

Abstract

Novel approaches were proposed for constructing simultaneous confidence intervals for all differences of coefficients of variation of log-normal distributions, using the method of variance estimates recovery (MOVER) approach and the computational approach. They are then compared with the fiducial generalized confidence interval (FGCI) approach which was presented by (W. Thangjai, S. Niwitpong and S. Niwitpong, Simultaneous fiducial generalized confidence intervals for all differences of coefficients of variation of log-normal distributions, Lecture Notes in Artificial Intelligence, 2016). A Monte Carlo simulation was conducted to compare the performances of these simultaneous confidence intervals based on the coverage probability and average length. Simulation results show that the MOVER approach is satisfactory performances for all sample case ($k$) and sample size ($n$). Moreover, the computational approach performs as well as the MOVER approach when the sample size is large. Our approaches are applied to an analysis of a real data set from rainfall in regions of Thailand.

Keywords

• average length,computational approach,coverage probability,MOVER approach,simulation

References

1. [1] A.H. Abdel-Karim, Construction of simultaneous confidence intervals for ratios of means of lognormal distributions, Comm. Statist. Simulation Comput. 44 (2), 271- 283, 2015.
2. [2] S. Aghadoust, K. Abdollahnezhad, F. Yaghmaei and A.A. Jafari, Comparison of some different methods for hypothesis test of means of log-normal populations, arXiv:1508.01782v1 [stat.ME], 2015.
3. [3] R. Ananthakrishnan and K. Soman, Statistical distribution of daily rainfall and its association with the coefficient of variation of rainfall series, Int. J. Climatol. 9 (5), 485-500, 1989.
4. [4] H.K. Cho, K.P. Bowman and G.R. North, A comparison of gamma and lognormal distributions for characterizing satellite rain rates from the tropical rainfall measuring mission, J. Appl. Meteor. 43 (11), 1586-1597, 2004.
5. [5] P. De, J.B. Ghosh and C.E. Wells, Scheduling to minimize the coefficient of variation, Int. J. Production Economics 44 (3), 249-253, 1996.
6. [6] A. Donner and G.Y. Zou, Closed-form confidence intervals for function of the normal standard deviation, Stat. Methods Med. Res. 21 (4), 347-359, 2010.
7. [7] E.Y. Gokpinar, E. Polat, F. Gokpinar and S. Gunay, A new computational approach for testing equality of inverse Gaussian means under heterogeneity, Hacet. J. Math. Stat. 42 (5), 581-590, 2013.
8. [8] F. Gokpinar and E. Gokpinar, A computational approach for testing equality of coef- ficients of variation in k normal populations, Hacet. J. Math. Stat. 44 (5), 1197-1213, 2015.

9. [9] J. Hannig, H. Iyer and P. Patterson, Fiducial generalized confidence intervals, J. Amer. Statist. Assoc. 101 (473), 254-269, 2006.
10. [10] J. Hannig, E. Lidong, A. Abdel-Karim and H. Iyer, Simultaneous fiducial generalized confidence intervals for ratios of means of lognormal distributions, Austrian J. Stat. 35 (2&3), 261-269, 2006.
11. [11] M.S. Hasan and K. Krishnamoorthy, Improved confidence intervals for the ratio of coefficients of variation of two lognormal distributions, J. Stat. Theory Appl. 16 (3), 345-353, 2017.
12. [12] A.A. Jafari and K. Abdollahnezhad, Inferences on the means of two log-normal dis- tributions: A computational approach test, Comm. Statist. Simulation Comput. 44 (7), 1659-1672, 2015.
13. [13] S.A. Joulious and C.A.M. Debarnot, Why are pharmacokinetics data summarize by arithmetic means?, J. Biopharm. Stat. 10 (1), 55-71, 2000.
14. [14] A.L. Koch, The logarithm in biology, J. Theor. Biol. 12 (2), 276-290, 1966.
15. [15] J.M. Nam and D. Kwon, Inference on the ratio of two coefficients of variation of two lognormal distributions, Comm. Statist. Theory Methods 46 (17), 8575-8587, 2017.
16. [16] S. Niwitpong, Confidence intervals for coefficient of variation of lognormal distribu- tion with restricted parameter space, Appl. Math. Sci. 7 (77), 3805-3810, 2013.
17. [17] N. Pal, W.K. Lim and C.H. Ling, A computational approach to statistical inferences, J. Appl. Probab. Stat. 2 (1), 13-35, 2007.
18. [18] H.P. Ritzema, Frequency and regression analysis, Wageningen, Netherlands, 1994.
19. [19] P. Sangnawakij, S. Niwitpong and S. Niwitpong, Confidence intervals for the ratio of coefficients of variation of the gamma distributions, Lecture Notes in Computer Science 9376, 193-203, 2015.
20. [20] S.M. Sadooghi-Alvandi and A. Malekzadeh, Simultaneous confidence intervals for ratios of means of several lognormal distributions: A parametric bootstrap approach, Comput. Statist. Data Anal. 69 (C), 133-140, 2014.
21. [21] P. Sangnawakij and S. Niwitpong, Confidence intervals for coefficients of variation in two-parameter exponential distributio, Comm. Statist. Simulation Comput. 46 (8), 6618-6630, 2017.
22. [22] F. Schaarschmidt, Simultaneous confidence intervals for multiple comparisons among expected values of log-normal variables, Comput. Statist. Data Anal. 58, 265-275, 2013.
23. [23] H. Shen, L. Brown and Z. Hui, Efficient estimation of log-normal means with appli- cation to pharmacokinetics data, Stat. Med. 25 (17), 3023-3038, 2006.
24. [24] W. Thangjai, S. Niwitpong and S. Niwitpong, Simultaneous fiducial generalized con- fidence intervals for all differences of coefficients of variation of log-normal distribu- tions, Lecture Notes in Artificial Intelligence 9978, 552-561, 2016.
25. [25] L. Tian, Inferences on the common coefficient of variation, Stat. Med. 24 (14), 2213- 2220, 2005.
26. [26] M.G. Vangel, Confidence intervals for a normal coefficient of variation, J. Amer. Statist. Assoc. 50 (1), 21-26, 1996.
27. [27] A.C.M. Wong and J. Wu, Small sample asymptotic inference for the coefficient of variation: Normal and nonnormal models, J. Statist. Plann. Inference 104 (1), 73- 82, 2002.
28. [28] G. Zhang and B. Falk, Inference of several log-normal distributions, Technical Report, 2014.
29. [29] G.Y. Zou and A. Donner, Construction of confidence limits about effect measures: A general approach, Stat. Med. 27 (10), 1693-1702, 2008.
30. [30] G.Y. Zou, J. Taleban and C.Y. Hao, Confidence interval estimation for lognormal data with application to health economics, Comput. Statist. Data Anal. 53 (11), 3755-3764, 2009.