Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P518

In this paper, we proposes confidence intervals for the ratio of normal means with one variance unknown based on the generalized confidence interval (GCI) approach, the method of variance estimates recovery (MOVER), and a Bootstrap technique (Bootstrap confidence interval (BCI). The coverage probabilities and expected lengths of these confidence intervals were then compared via a Monte Carlo simulation.The simulation results indicated that the MOVER approaches are satisfactory in terms of the coverage probability. The results indicate that the MOVER confidence intervals are better than those constructed via the GCI and BCI. The expected lengths of the MOVER approach are shorter than expected lengths of GCI and BCI. The coverage probabilities of the MOVER confidence intervals are more appropriate than those using the GCI and BCI. Simulation results show that the MOVER approach is satisfactory performances for all sample case which was presented by Thangjai et al. [19]. Our approaches are applied to an analysis of a real data set of drugs or treatments.

[1] A. Donner and G. Zou, “Closed-Form confidence intervals for functions of the normal mean and standard deviation,” Stat. Methods Med. Res., vol. 21, pp. 347-359, 2010.

[2] EC. Fieller, “Some problems in interval estimation. Journal of the Royal Statistical Society,” Series B (Methodological), vol. 16, pp. 175-185, 1954.

[3] C. Galeone and A. Pollastri, “Confidence intervals for the ratio of two means using the distribution of the quotient of two normal,” SiT., pp. 451-472, 2012.

[4] HK. Iyer and PD. Patterson, “A recipe for constructing generalized pivotal quantities and generalized confidence intervals,” Technical Report, 2002.

[5] M.A. Koschat, “A Characterization of the Fieller solution,” Ann. Stat. 15 (1), pp. 462-468, 1987.

[6] K. Krishnamoorthy and T. Mathew, Statistical Tolerance Regions: Theory, Application, and Computation. John Wilay & Sons, Inc.: New Jersey, USA., 2001.

[7] JC. Lee and S. Lin, “Generalized confidence intervals for the ratio of means of two normal populations,” J. Stat. Plan. Infer., 123, pp. 49-60, 2004.

[8] P. Liqian and T. Tiejun, “A note on a two-sample T test one variance unknown,” Stat. Methodol., vol. 8, pp. 528-534, 2011.

[9] HQ. Li, “Confidence intervals for ratio of two poisson rates using the method of variance estimates recovery,” Computational Statistics., vol. 29, pp. 869-889, 2014.

[10] A. Maity and M. Sherman, “The two sample t-test with one variance unknown,” Am. Stat., vol. 60, pp. 163-166, 2006.

[11] DC. Montgomery and GC. Runger, Applied Statistics and Probability for Engineers, 3rd edition, John Wilay & Sons, Inc.: New York, USA., 2003.

[12] S. Niwitpong, “Confidence intervals for the difference of two normal population means with one variance unknown,” Thailand Statistician Journal., vol. 7, pp. 161-177, 2009.

[13] S. Niwitpong, “A simple confidence interval for the difference between two normal population means with one variance unknown,” I JASP., vol. 1, pp. 102-109, 2013.

[14] S. Niwitpong, “Confidence intervals for the difference and the ratio of lognormal means with bounded parameters,” Songklanakarin Journal of Science and Technology 37:231-240, 2015.

[15] S. Niwitpong, “Confidence intervals for the difference and the ratio of coefficients of variation of normal distribution with a known ratio of variances,” IJMTT., vol. 29, pp. 13-20, 2016.

[16] S. Sodanin, “Generalized confidence intervals for the normal mean with unknown coefficient of variation,” AIP Conference Proceeding 1175:030043-1-030043-8, 2016.

[17] P. Sangnawakij and S. Niwitpong, “Confidence intervals for coefficients of variation in two-parameter exponential distribution,” Commun. Stat. Simul. Comput. 46 (8), 66186630, 2017.

[18] W. Thangjai, S. Niwitpong, and S. Niwitpong, “Simultaneous confidence intervals for all differences of means of normal distributions with unknown coefficients of variation,” International conference of the Thailand ecomometrics society TES 2018 : Predictive Econometrics and Big Data, pp. 670-682, 2018.

[19] W. Thangjai, S. Niwitpong, and S. Niwitpong, “Simultaneous Confidence intervals for all differences of coefficients of variation of lonormal distributions,” Hacet. J. Math. Stat., pp. 1-17, 2019.

[20] S. Weerahandi, “Generalized confidence intervals,” JASA., vol. 88, pp. 899-905, 1993.

[21] A. Wongkhao, “Confidence intervals for parameters of normal distribution,” Ph.D. Stat. thesis, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand, 2014.

[22] A. Wongkhao, “Confidence intervals for the ratio of two independent coefficients of variation of normal distribution,” FJMS., vol. 98 (6), pp. 741-757, 2015.

[23] X-H. Zhou and W. Tu, “Interval estimation for the ratio in means of log-normally distributed medical costs with zero values,” Comput.Stat. Data.An., vol. 35, pp. 201-210, 2000.

Sukritta Sodanin, Suparat Niwitpong, "Confidence Intervals for the Ratio of the Means of Two Normal Distributions with One Variance Unknown," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 66, no. 1, pp. 148-156, 2020. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V66I1P518