Constructing a confidence interval for the ratio of normal distribution quantiles

References

[1] K. Abdollahnezhad and A. A. Jafari, Testing the equality of quantiles for several normal populations, Comm. Statist. Simulation Comput. 47 (2018), no. 7, 1890–1898. 10.1080/03610918.2017.1332209Search in Google Scholar

[2] W. Albers and P. Löhnberg, An approximate confidence interval for the difference between quantiles in a bio-medical problem, Stat. Neerl. 38 (1984), no. 1, 20–22. 10.1111/j.1467-9574.1984.tb01093.xSearch in Google Scholar

[3] R. L. Berger and J. C. Hsu, Bioequivalence trials, intersection-union tests and equivalence confidence sets, Stat. Neerl. 11 (1996), no. 4, 283–319. 10.1214/ss/1032280304Search in Google Scholar

[4] D. R. Bristol, Distribution-free confidence intervals for the difference between quantiles, Stat. Neerl. 44 (1990), no. 2, 87–90. 10.1111/j.1467-9574.1990.tb01530.xSearch in Google Scholar

[5] S. Chakraborti and J. Li, Confidence interval estimation of a normal percentile, Amer. Statist. 61 (2007), no. 4, 331–336. 10.1198/000313007X244457Search in Google Scholar

[6] S. C. Chow and J. P. Liu, On assessment of bioequivalence under a higher-order crossover design, J. Biopharmaceutical Stat. 2 (1992), no. 2, 239–256. 10.1080/10543409208835042Search in Google Scholar PubMed

[7] T. F. Cox and K. Jaber, Testing the equality of two normal percentiles, Comm. Statist. Simulation Comput. 14 (1985), no. 2, 345–356. 10.1080/03610918508812443Search in Google Scholar

[8] E. C. Fieller, A fundamental formula in the statistics of biological assay, and some applications, Quart. J. Pharm. 17 (1944), 117–123. Search in Google Scholar

[9] D. J. Finney, Statistical Method in Biological Assay, Griffin, London, 1978. Search in Google Scholar

[10] H. Guo and K. Krishnamoorthy, Comparison between two quantiles: The normal and exponential cases, Comm. Statist. Simulation Comput. 34 (2005), no. 2, 243–252. 10.1081/SAC-200055639Search in Google Scholar

[11] I. J. Hall, Approximate one-sided tolerance limits for the difference or sum of two independent normal variates, J. Qual. Technol. 16 (1984), no. 1, 15–19. 10.1080/00224065.1984.11978882Search in Google Scholar

[12] L.-F. Huang, Approximated non-parametric confidence regions for the ratio of two percentiles, Comm. Statist. Theory Methods 46 (2017), no. 8, 4004–4015. 10.1080/03610926.2015.1076479Search in Google Scholar

[13] L.-F. Huang and R. A. Johnson, Confidence regions for the ratio of percentiles, Statist. Probab. Lett. 76 (2006), no. 4, 384–392. 10.1016/j.spl.2005.08.034Search in Google Scholar

[14] R. A. Johnson and L.-F. Huang, Some exact and approximate confidence regions for the ratio of percentiles from two different distributions, Mathematical and Statistical Methods in Reliability (Trondheim 2002), Ser. Qual. Reliab. Eng. Stat. 7, World Scientific, River Edge (2003), 455–468. 10.1142/9789812795250_0029Search in Google Scholar

[15] K. Krishnamoorthy, Modified normal-based approximation to the percentiles of linear combination of independent random variables with applications, Comm. Statist. Simulation Comput. 45 (2016), no. 7, 2428–2444. 10.1080/03610918.2014.904342Search in Google Scholar

[16] K. Krishnamoorthy and E. Oral, Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean, Stat. Methods Med. Res. 26 (2017), no. 6, 2919–2937. 10.1177/0962280215615160Search in Google Scholar

[17] J. C. Lee and S.-H. Lin, Generalized confidence intervals for the ratio of means of two normal populations, J. Statist. Plann. Inference 123 (2004), no. 1, 49–60. 10.1016/S0378-3758(03)00141-1Search in Google Scholar

[18] A. Malekzadeh and A. A. Jafari, Inference on the equality means of several two-parameter exponential distributions under progressively Type-II censoring, Comm. Statist. Simulation Comput. 12 (2018), no. 4, 776–793. 10.1080/03610918.2018.1538452Search in Google Scholar

[19] A. Malekzadeh and M. Kharrati-Kopaei, Inferences on the common mean of several heterogeneous log-normal distributions, J. Appl. Stat. 46 (2019), no. 6, 1066–1083. 10.1080/02664763.2018.1531980Search in Google Scholar

[20] A. Malekzadeh and M. Kharrati-Kopaei, Simultaneous confidence intervals for the quantile differences of several two-parameter exponential distributions under the progressive type II censoring scheme, J. Stat. Comput. Simul. 90 (2020), no. 11, 2037–2056. 10.1080/00949655.2020.1762084Search in Google Scholar

[21] A. Malekzadeh and K. Sabri-Laghaie, Quantile-based reliability comparison of products: Applied to log-normal distribution, Comm. Statist. Simulation Comput. (2019), 10.1080/03610918.2019.1600706. 10.1080/03610918.2019.1600706Search in Google Scholar

[22] A. W. Marshall and J. E. Walsh, Some test for comparing percentage points of two arbitrary continuous populations. I, Report, 1950. Search in Google Scholar

[23] J. Poirier, G. Y. Zou and J. Koval, Confidence intervals for a difference between lognormal means in cluster randomization trials, Stat. Methods Med. Res. 26 (2017), no. 2, 598–614. 10.1177/0962280214552291Search in Google Scholar PubMed

[24] S. Rudolfer and M. Campbell, Large sample inference for diagnostic normal limits in gaussian populations, Comm. Statist. Theory Methods 14 (1985), no. 8, 1801–1835. 10.1080/03610928508829015Search in Google Scholar

[25] J. E. Walsh, Bounded significance level tests for comparing quantiles of two possibly different continuous populations, Ann. Inst. Statist. Math. 6 (1955), 213–222. 10.1007/BF02905915Search in Google Scholar

[26] S. Weerahandi, Exact Statistical Methods for Data Analysis, Springer Ser. Statist., Springer, New York, 1995. 10.1007/978-1-4612-0825-9Search in Google Scholar

[27] S. Weerahandi and R. A. Johnson, Testing reliability in a stress-strength model when X and Y are normally distributed, Technometrics 34 (1992), no. 1, 83–91. 10.2307/1269555Search in Google Scholar

[28] G. Y. Zou and A. Donner, Construction of confidence limits about effect measures: A general approach, Stat. Med. 27 (2008), no. 10, 1693–1702. 10.1002/sim.3095Search in Google Scholar PubMed

[29] G. Y. Zou, J. Taleban and C. Y. Huo, Confidence interval estimation for lognormal data with application to health economics, Comput. Statist. Data Anal. 53 (2009), no. 11, 3755–3764. 10.1016/j.csda.2009.03.016Search in Google Scholar