Confidence Intervals for the Coefficients of Variation with Bounded Parameters
In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.
[1] R. Mahmoudvand, and H. Hassani, “Two new confidence intervals for
the coefficients of variation in a normal distribution,” Journal of Applied
Statistics, vol. 36, no. 4, pp. 429–442, Apr. 2009.
[2] E. G. Miller, “Asymptotic test statistics for coefficient of variation,”
Communication in Statistic-Theory & Methods, vol. 20, no. 10, pp.
3351–3363, 1991.
[3] A. A. Jafari, and J. Behboodian, “Two approachs for comparing the
Coefficients of Variation of Several Normal Populations,” World
Applied Sciences Journal, vol. 10, no. 7, pp. 853–857, 2010.
[4] W. Reh, and B. Scheffler, “Significance Tests and Confidence
Intervalsfor Coefficients of Variation,” The Statistical Software
Newsletter, pp. 449–452, 1996.
[5] S. Verrill, and R. A. Johnson, “Confidence Bounds and Hypothesis Tests
for Normal Distribution Coefficient of Variation,” Research Paper FPLRP-
638, Madison, U. S. Department of Agriculture, Forest Service,
Forest Products Labaratory: 57 p, 2007.
[6] K. S. Nairy, and K. A. Rao, “Tests of coefficients of normal population,”
Communications in Statistics-Simulation and Computation, vol.32, pp.
641–661, 2003.
[7] K. Kelly, “Sample Size Planning for the Coefficient of Variation from
the Accuracy in Parameter Estimation Approach,” Behavior Research
Methods, vol. 39, no. 4, pp. 755–766, 2007.
[8] G. J. Feldman, and R. D. Cousins, “Unified approach to the classical
statistical analysis of small signals,” Physical Previews D, vol. 57,
3873–3889, 1998.
[9] B. P. Roe, and M. B. Woodroofe, “Setting confidence belts,” Physical
Previews D, vol. 60, pp. 3009–3015, 2000.
[10] V. Giampaoli, and J. M. Singer, “Comparison of two normal populations
with restricted means,” Computational Statistics & Data Analysis, vol.
46, pp. 511–529, 2004.
[11] S. N. Evans, B. B. Hansen, and P. B. Stark, “Minimax expected measure
confidence sets for restricted location parameters.”Bernoulli, vol. 11, pp.
571–590, 2005.
[12] S. Niwitpong, “Confidence intervals for the mean of Lognormal
distribution with restricted parameter space,” Applied Mathematical
Sciences, vol. 7, pp. 161–166, 2012.
[13] J. D. Curto, and J. C. Pinto, “The coefficient of variation asymptotic
distribution in case of non-iid random variables,” Journal ofApplied
Statistics, vol. 36, no. 1, pp. 21–32, 2009.
[14] S. Banik, and B. M. G. Kibrie, “Estimating the population coefficient of
variation by confidence intervals,” Communications in Statistics-
Simulation and Computation, vol.40, no. 8, pp. 1236–1261, 2011.
[15] A. Donner, and G. Y. Zou, “Closed-form confidence intervals for
functions of the normal mean and standard deviation,” Statistical
Methods in Medical Research, vol. 21, no. 4, pp. 347–359, 2010.
[16] J. Forkman, “Statistical Inference for the Coefficient of Variation in
Normally Distributed Data,” Research Report, Centre of Biostochastics,
Swedish University of Agricultural Sciences: 29 p, 2006.
[17] A. T. McKay, “Distribution of the Coefficient of Variation and the
Extended t Distribution,” Journal of the Royal Statistics Society, vol. 95,
pp. 695–698, 1932.
[18] M. G. Vangel, “Confidence Intervals for a Normal Coefficient of
Variation,” The American Statistician, vol.50, no. 1, pp. 21–26, 1996.
[19] H. Wang, “Confidence intervals for the mean of a normal distribution
with restricted parameter spaces,” Journal of Statistical Computation and
Simulation, vol. 78, pp. 829–841, 2008.
[20] S. Niwitpong, “Coverage probability of confidence intervals for the
normal mean and variance with restricted parameter space,” in 2011
Proc. WASET, pp. 540–545.
[21] L. H. Koopmans, D. B. Owen, and J. I. Rosenblatt, “Confidence interval
for the coefficient of variation for the normal and lognormal
distributions,” Biometrika, vol. 51, no. 1-2, pp. 25-32, 1964.
[1] R. Mahmoudvand, and H. Hassani, “Two new confidence intervals for
the coefficients of variation in a normal distribution,” Journal of Applied
Statistics, vol. 36, no. 4, pp. 429–442, Apr. 2009.
[2] E. G. Miller, “Asymptotic test statistics for coefficient of variation,”
Communication in Statistic-Theory & Methods, vol. 20, no. 10, pp.
3351–3363, 1991.
[3] A. A. Jafari, and J. Behboodian, “Two approachs for comparing the
Coefficients of Variation of Several Normal Populations,” World
Applied Sciences Journal, vol. 10, no. 7, pp. 853–857, 2010.
[4] W. Reh, and B. Scheffler, “Significance Tests and Confidence
Intervalsfor Coefficients of Variation,” The Statistical Software
Newsletter, pp. 449–452, 1996.
[5] S. Verrill, and R. A. Johnson, “Confidence Bounds and Hypothesis Tests
for Normal Distribution Coefficient of Variation,” Research Paper FPLRP-
638, Madison, U. S. Department of Agriculture, Forest Service,
Forest Products Labaratory: 57 p, 2007.
[6] K. S. Nairy, and K. A. Rao, “Tests of coefficients of normal population,”
Communications in Statistics-Simulation and Computation, vol.32, pp.
641–661, 2003.
[7] K. Kelly, “Sample Size Planning for the Coefficient of Variation from
the Accuracy in Parameter Estimation Approach,” Behavior Research
Methods, vol. 39, no. 4, pp. 755–766, 2007.
[8] G. J. Feldman, and R. D. Cousins, “Unified approach to the classical
statistical analysis of small signals,” Physical Previews D, vol. 57,
3873–3889, 1998.
[9] B. P. Roe, and M. B. Woodroofe, “Setting confidence belts,” Physical
Previews D, vol. 60, pp. 3009–3015, 2000.
[10] V. Giampaoli, and J. M. Singer, “Comparison of two normal populations
with restricted means,” Computational Statistics & Data Analysis, vol.
46, pp. 511–529, 2004.
[11] S. N. Evans, B. B. Hansen, and P. B. Stark, “Minimax expected measure
confidence sets for restricted location parameters.”Bernoulli, vol. 11, pp.
571–590, 2005.
[12] S. Niwitpong, “Confidence intervals for the mean of Lognormal
distribution with restricted parameter space,” Applied Mathematical
Sciences, vol. 7, pp. 161–166, 2012.
[13] J. D. Curto, and J. C. Pinto, “The coefficient of variation asymptotic
distribution in case of non-iid random variables,” Journal ofApplied
Statistics, vol. 36, no. 1, pp. 21–32, 2009.
[14] S. Banik, and B. M. G. Kibrie, “Estimating the population coefficient of
variation by confidence intervals,” Communications in Statistics-
Simulation and Computation, vol.40, no. 8, pp. 1236–1261, 2011.
[15] A. Donner, and G. Y. Zou, “Closed-form confidence intervals for
functions of the normal mean and standard deviation,” Statistical
Methods in Medical Research, vol. 21, no. 4, pp. 347–359, 2010.
[16] J. Forkman, “Statistical Inference for the Coefficient of Variation in
Normally Distributed Data,” Research Report, Centre of Biostochastics,
Swedish University of Agricultural Sciences: 29 p, 2006.
[17] A. T. McKay, “Distribution of the Coefficient of Variation and the
Extended t Distribution,” Journal of the Royal Statistics Society, vol. 95,
pp. 695–698, 1932.
[18] M. G. Vangel, “Confidence Intervals for a Normal Coefficient of
Variation,” The American Statistician, vol.50, no. 1, pp. 21–26, 1996.
[19] H. Wang, “Confidence intervals for the mean of a normal distribution
with restricted parameter spaces,” Journal of Statistical Computation and
Simulation, vol. 78, pp. 829–841, 2008.
[20] S. Niwitpong, “Coverage probability of confidence intervals for the
normal mean and variance with restricted parameter space,” in 2011
Proc. WASET, pp. 540–545.
[21] L. H. Koopmans, D. B. Owen, and J. I. Rosenblatt, “Confidence interval
for the coefficient of variation for the normal and lognormal
distributions,” Biometrika, vol. 51, no. 1-2, pp. 25-32, 1964.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65105", author = "Jeerapa Sappakitkamjorn and Sa-aat Niwitpong", title = "Confidence Intervals for the Coefficients of Variation with Bounded Parameters", abstract = "In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.
", keywords = "Bounded parameters, coefficient of variation, confidence interval, Monte Carlo simulation. ", volume = "7", number = "9", pages = "1416-6", }
