Confidence Interval for The Coefficient of Variation in A Normal Distribution with A Known Population Mean after A Preliminary T Test
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Published:
Mar 30, 2018
Keywords:
measure of dispersion, preliminary test, coverage probability, expected length, simulation study
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Abstract
This paper proposes the confidence interval for the coefficient of variation in a normal distribution with a known population mean after a preliminary T test. This has applications when one knows the population mean of a control group. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed confidence interval with two existing confidence intervals. Two performance measures were used to assess the confidence interval for the coefficient of variation, namely: coverage probability and expected length. Simulation results showed that the proposed confidence interval performs well in terms of coverage probability and expected length compared with two existing confidence intervals. A real data example presenting the melting point of beeswax from 59 sources was used for illustration and performing a comparison.
Keywords: measure of dispersion, preliminary test, coverage probability, expected length, simulation study.
Corresponding author: E-mail : wararit@mathstat.sci.tu.ac.th
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References
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[33] Panichkitkosolkul, W., 2013. Confidence intervals for the coefficient of variation in a normal distribution with a known population mean, Journal of Probability and Statistics, Article ID 324940, 11 pages, doi:10.1155/2013/324940
[34] Paksaranuwat, P., and Niwitpong, S., 2009. Confidence intervals for the difference between two means with missing data following a preliminary test, Science Asia, 35, 310-313.
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[36] Chiou, P., and Han, C.P., 1995. Interval estimation of error variance following a preliminary test in one-way random model, Communications in Statistics-Simulation and Computation, 24, 817-824.
[37] Panichkitkosolkul, W., and Niwitpong, S., 2011. On multistep-ahead prediction intervals following unit root tests for a Gaussian AR(1) process with additive outliers, Applied Mathematical Sciences, 5, 2297-2316.
[38] Panichkitkosolkul, W., and Niwitpong, S., 2012. Prediction intervals for the Gaussian autoregressive processes following the unit root tests, Model Assisted Statistics and Applications: An International Journal, 7, 1-15.
[39] Ihaka, R., and Gentleman, R.R., 1996. A Language for data analysis and graphics, Journal of Computational and Graphical Statistics, 5, 299-314.
[40] Development Core Team, R., 2014. An Introduction to R, Vienna, R Foundation for Statistical Computing.
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[42] White, J., Riethof, M., and Kushnir, I., 1960. Estimation of microcrystalline wax in beeswax, Journal of the Association of Official Analytical Chemists, 43, 781-790.
[43] Rice, J.A., 2007. Mathematical Statistics and Data Analysis, California, Duxbury Press.
[2] Nairy, K.S., and Rao, K.A., 2003. Tests of coefficients of variation of normal population, Communication in Statistics-Simulation and Computation, 32, 641-661.
[3] Ahn, K., 1995. Use of coefficient of variation for uncertainty analysis in fault tree analysis, Reliability Engineering and System Safety, 47, 229-230.
[4] Gong, J., and Li, Y., 1999. Relationship between the estimated Weibull modulus and the coefficient of variation of the measured strength for ceramics, Journal of the American Ceramic Society, 82, 449-452.
[5] Faber, D.S., and Korn, H., 1991. Applicability of the coefficient of variation method for analyzing synaptic plasticity, Biophysical Society, 60, 1288-1294.
[6] Hamer, A.J., Strachan, J.R.., Black, M.M., Ibbotson, C., and Elson, R.A., 1995. A new method of comparative bone strength measurement, Journal of Medical Engineering and Technology, 19, 1-5.
[7] Billings, J., Zeitel, L., Lukomink, J., Carey, T.S., Blank, A.E., and Newman, L., 1993. Impact of socioeconomic status of hospital use in New York City, Health Affairs, 12, 162-173.
[8] Miller, E.G., and Karson, M.J., 1977. Testing the equality of two coefficients of variation, American Statistical Association: Proceedings of the Business and Economics Section, Part I, 278-283.
[9] Worthington, A.C., and Higgs, H., 2003. Risk, return and portfolio diversification in major painting markets: the application of conventional financial analysis to unconventional investments, Discussion Papers No.148 in Economics, Finance and International Competitiveness, School of Economics and Finance, Queensland University of Technology.
[10] Pyne, D.B., Trewin, C.B., and Hopkins, W.G., 2004. Progression and variability of competitive performance of Olympic swimmers, Journal of Sports Sciences, 22, 613-620.
[11] Smithson, M., 2001. Correct confidence intervals for various regression effect sizes and parameters: the importance of noncentral distributions in computing intervals, Educational and Psychological Measurement, 61, 605-632.
[12] Thompson, B., 2002. What future quantitative social science research could look like: Confidence intervals for effect sizes, Educational Researcher, 31, 25-32.
[13] Steiger, J.H., 2004. Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis, Psychological Methods, 9, 164-182.
[14] McKay, A.T., 1932. Distribution of the coefficient of variation and the extended t distribution, Journal of the Royal Statistics Society, 95, 695-698.
[15] Fieller, E.C. 1932. A numerical test of the adequacy of A.T. McKay’s approximation, Journal of the Royal Statistical Society, 95, 699-702.
[16] Iglewicz, B., 1967. Some properties of the coefficient of variation, Ph.D. thesis, Virginia Polytechnic Institute.
[17] Iglewicz, B., and Myers, R.H., 1970. Comparisons of approximations to the percentage points of the sample coefficient of variation, Technometrics, 12, 166-169.
[18] Pearson, E.S., 1932. Comparison of A.T. McKay’s approximation with experimental sampling results, Journal of the Royal Statistics Society, 95, 703-704.
[19] Umphrey, G.J., 1983. A comment on McKay’s approximation for the coefficient of variation, Communications in Statistics-Simulation and Computation, 12, 629-635.
[20] Vangel, M.G., 1996. Confidence intervals for a normal coefficient of variation, The American Statistician, 15, 21-26.
[21] Panichkitkosolkul, W., 2009. Improved confidence intervals for a coefficient of variation of a normal distribution, Thailand Statistician, 7, 193-199.
[22] Sharma, K.K., and Krishna,H., 1994 Asymptotic sampling distribution of inverse coefficient- of-variation and its applications, IEEE Transactions on Reliability, 43, 630-633.
[23] Miller, E.G., 1991. Asymptotic test statistics for coefficient of variation, Communications in Statistics Theory and Methods, 20, 3351-3363.
[24] Ng, K.C., 2006. Performance of three methods of interval estimation of the coefficient of variation, InterStat Available at http://interstat.statjournals.net/ YEAR/2006/ articles/ 0609002.
[25] Mahmoudvand, R., and Hassani, H., 2009. Two new confidence intervals for the coefficient of variation in a normal distribution, Journal of Applied Statistics, 36, 429-442.
[26] Albatineh, A.N., Kibria, B.M.G., Wilcox, M.L., and Zogheib, B., 2014. Confidence interval estimation for the population coefficient of variation using ranked set sampling, Journal of Applied Statistics, 41, 733-751.
[27] Koopmans, L.H., Owen, D.B., and Rosenblatt, J.I., 1964. Confidence intervals for the coefficient of variation for the normal and lognormal distributions, Biometrika, 51, 25-32.
[28] Verrill, S., 2003. Confidence bounds for normal and log-normal distribution coefficient of variation, Research Paper EPL-RP-609, U.S. Department of Agriculture Madison, Wisconsin, USA.
[29] Buntao, N., and Niwitpong, S., 2012. Confidence intervals for the difference of coefficients of variation for lognormal distributions and delta-lognormal distributions, Applied Mathematical Sciences, 6, 6691-6704.
[30] Vangel, M.G., 1996. Confidence intervals for a normal coefficient of variation, The American Statistician, 50, 21-26.
[31] Curto, J.D., and Pinto, J.C., 2009. The coefficient of variation asymptotic distribution in the case of non-iid random variables, Journal of Applied Statistics, 36, 21-32.
[32] Gulhar, M., Kibria, B.M.G., Albatineh, A.N., and Ahmed, N.U., 2012. A comparison of some confidence intervals for estimating the population coefficient of variation: a simulation study, SORT, 36, 45-68.
[33] Panichkitkosolkul, W., 2013. Confidence intervals for the coefficient of variation in a normal distribution with a known population mean, Journal of Probability and Statistics, Article ID 324940, 11 pages, doi:10.1155/2013/324940
[34] Paksaranuwat, P., and Niwitpong, S., 2009. Confidence intervals for the difference between two means with missing data following a preliminary test, Science Asia, 35, 310-313.
[35] Kabaila, P., and Farchione, D., 2012. The minimum coverage probability of confidence intervals in regression after a preliminary test, Journal of Statistical Planning and Inference, 142, 956-964.
[36] Chiou, P., and Han, C.P., 1995. Interval estimation of error variance following a preliminary test in one-way random model, Communications in Statistics-Simulation and Computation, 24, 817-824.
[37] Panichkitkosolkul, W., and Niwitpong, S., 2011. On multistep-ahead prediction intervals following unit root tests for a Gaussian AR(1) process with additive outliers, Applied Mathematical Sciences, 5, 2297-2316.
[38] Panichkitkosolkul, W., and Niwitpong, S., 2012. Prediction intervals for the Gaussian autoregressive processes following the unit root tests, Model Assisted Statistics and Applications: An International Journal, 7, 1-15.
[39] Ihaka, R., and Gentleman, R.R., 1996. A Language for data analysis and graphics, Journal of Computational and Graphical Statistics, 5, 299-314.
[40] Development Core Team, R., 2014. An Introduction to R, Vienna, R Foundation for Statistical Computing.
[41] Development Core Team, R., 2014. A Language and Environment for Statistical Computing. Vienna, R Foundation for Statistical Computing.
[42] White, J., Riethof, M., and Kushnir, I., 1960. Estimation of microcrystalline wax in beeswax, Journal of the Association of Official Analytical Chemists, 43, 781-790.
[43] Rice, J.A., 2007. Mathematical Statistics and Data Analysis, California, Duxbury Press.