Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

Theerapong Kaewprasert, Sa-Aat Niwitpong, Suparat Niwitpong

Abstract

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

Keywords

References

[1] R. Mahmoudvand and H. Hassani, “Two new confidence intervals for the coefficientof variation in a normal distribution,” Journal of Applied Statistics, vol. 36, pp. 429–442, 2009.
[2] M. G. Vangel, “Confidence intervals for a normal coefficient of variation,” The American Statistician, vol. 15, pp. 21–26, 1996.

[3] L. Tian, “Inferences on the common coefficient of variation,” Statistics in Medicine, vol. 24, pp. 2213–2220, 2005.

[4] S. Verrill and R. A. Johnson, “Confidence bounds and hypothesis tests for normal distribution coefficients of variation,” Communications in Statistics – Theory and Methods, vol. 36, pp. 2187–2206, 2007.

[5] P. Sangnawakij and S. Niwitpong, “Confidence intervals for coefficients of variation in two-parameter exponential distribuitons,” Communications in Statistics – Simulation and Computation, vol. 46, pp. 6618–6630, 2017.

[6] M. La-ongkaew, S. A. Niwitpong, and S. Niwitpong, “Confidence intervals for the difference between the coefficients of variation of Weibull distributions for analyzing wind speed dispersion,” PeerJ, vol. 9, pp. 1–24, 2021.

[7] N. Yosboonruang, S. A. Niwitpong, and S. Niwitpong, “Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: A study from Thailand,” PeerJ, vol. 7, pp. 1–21, 2019.

[8] P. Sangnawakij and S. Niwitpong, “Confidence intervals for functions of coefficients of variation with bounded parameter spaces in two gamma distributions,” Songklanakarin Journal of Science and Technology, vol. 39, pp. 27–39, 2017.

[9] A. Llera and C. F. Beckmann, “Estimating an inverse gamma distribution,” 2016. [Online]. Available: http://arXiv:1605.01019v2 [10] S. H. Abid and S. A. Al-Hassany, “On the inverted gamma distribution,” International Journal of Systems Science and Applied Mathematics, vol. 1, pp. 16–22, 2016.

[11] J. Sun, Y-Y. Zhang, and Y. Sun, “The empirical Bayes estimators of the rate parameter of the inverse gamma distribution with a conjugate inverse gamma prior under Stein's loss function,” Journal of Statistical Computation and Simulation, vol. 91, pp. 1504–1523, 2021.

[12] T. Kaewprasert, S. A. Niwitpong, and S. Niwitpong, “Confidence interval for coefficient of variation of inverse gamma distributions,” in Proceeding of Integrated Uncertainty in Knowledge Modelling and Decision Making, 2020, pp. 407–418.

[13] W. Puggard, S. A. Niwitpong, and S. Niwitpong, “Generalized confidence interval of the ratio of coefficient of variation of Birnbaum-Saunders distributions,” in Proceeding of Integrated Uncertainty in Knowledge Modelling and Decision Making, 2020, pp. 398–406.

[14] N. Yosboonruang and S. Niwitpong, “Statistical inference on the ratio of delta-lognormal coefficients of variation,” Applied Science and Engineering Progress, vol. 14, no. 3, pp. 489– 502, 2020, doi: 10.14416/j.asep.2020.06.003.

[15] M. S. Hasan and K. Krishnamoorthy, “Improved confidence intervals for the ratio of coefficients of variation of two lognormal distributions,” Journal of Statistical Theory and Applications, vol.16, pp. 345–353, 2017.

[16] J. Nam and D. Kwon, “Inference on the ratio of two coefficients of variation of two lognormal distributions,” Communications in Statistics - Theory and Methods, vol. 46, pp. 8575–8587, 2016.

[17] B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. London, England: Chapman and Hall, 1993, pp. 168–177.

[18] K. Krishnamoorthy and X. Wang, “Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases,” Environmetrics, vol. 27, pp. 479–493, 2016.

[19] E. B. Wilson and M. M. Hilferty, “The distribution of chi-squares,” in Proceedings of the National Academy of Science, 1931, pp. 684–688.

[20] H. Jeffreys, Theory of probability, 3rd ed. London, England: Oxford University Press, 1961.

[21] S. Dongchu and Y. Keying, “Frequentist validity of posterior quantiles for a two-parameter exponential family,” Biometrika, vol. 83, pp. 55– 65, 1996.

[22] R. Yang and J. O. Berger, “A catalog of noninformative priors,” 1998. [Online]. Available: http://www.stats.org.uk/priors/noninformative/ YangBerger1998.pdf

[23] R Core Team, “An introduction to R: A programming environment for data analysis and graphics,” 2020. [Online]. Available: http:// cran.r-project.org/

[24] Upper Northern Region Irrigation Hydrology Center, “Rainfall data,” 2021. [Online]. Available: http://hydro-1.rid.go.th/

Full Text: PDF

DOI: 10.14416/j.asep.2021.12.002

Refbacks

There are currently no refbacks.

Username
Password
Remember me