Confidence Intervals for a Ratio of Two Population Medians by Price and Bonett Bootstrap-t Method
Article Sidebar
Main Article Content
Abstract
The confidence intervals for a ratio of two population medians are proposed and compared with the approximate confidence interval of the Price and Bonett. The proposed methods are modified from the Bonett method with the bootstrap-t method and the bootstrap percentile method. The Monte Carlo simulation technique was performed 5,000 times repeatedly, along with a round of random sampling using the bootstrap method 5,000 times. The simulation involved both data from the population with the non-normal distribution and the small size of each sample by using the R program. The results indicated that for all studied distributions, the Price and Bonett bootstrap-t confidence interval and the bootstrap percentile confidence interval performance were superior to the Price and Bonett confidence interval in 18 out of 24 case studies or 75% of case studies. The most important result of this study was that both groups showed high skewness and high kurtosis, and the Price and Bonett bootstrap-t confidence interval and the bootstrap percentile confidence interval performance were superior to the Price and Bonett confidence interval in all the studied cases.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The articles published are the opinion of the author only. The author is responsible for any legal consequences. That may arise from that article.
References
A. Tongkaw, “The development of confidence interval of difference median for two population with free-distributions by price bonett bootstrap-t method,” The Journal of KMUTNB, vol. 29, no. 1, pp. 124–134, 2019 (in Thai).
R. M. Price and D. G. Bonett, “Distribution-free confidence intervals for difference and ratio of medians,” Journal of Statistical Computation and Simulation, vol. 72, no. 2, pp. 119–124, 2002.
J. L. Wang and T. P. Hettmansperger, “Two-sample inference for median survival times based on one-sample procedures for censored survival data,” Journal of the American Statistical Association, vol. 85, no. 410, pp. 529–536, 1990.
L. J. Wei and M. H. Gail, “Nonparametric estimation for a scale-change with censored observations,” Journal of the American Statistical Association, vol.78, no. 382, pp. 382–388, 1983.
R. M. Price and D. G. Bonett, “Estimating the variance of the sample median,” Journal of Statistical Computation and Simulation, vol. 68, no. 3, pp. 295–305, 2001.
T. P. Hettmansperger and J. W. McKean, Robust Nonparametric Statistical Methods. New York: Wiley, 1998.
T. P. Hettmansperger and S. J. Sheather, “Confidence intervals based on interpolated order statistics,” Statistics & Probability Letters, vol. 4, no. 2, pp. 75–79, 1986.
B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap. New York: CRC press, 1994.
A. Tongkaw, “Confidence interval of one population variance by Bonett bootstrap-t method for non-normal distributions,” RMUTSB Academic Journal, vol. 5, no. 1, pp. 11–19, 2017 (in Thai).
D. G. Bonett, “Approximate confidence interval for standard deviation of nonnormal distributions,” Computational Statistics & Data Analysis, vol. 50, no. 3, pp. 775–782, 2006.
W. Panichkitkosolkul, “Improved confidence intervals for a coefficient of variation of a normal distribution,” Thailand Statistician. vol. 7, no. 2, pp. 193–199, 2009.