Confidence Intervals for the Difference of Two Normal Population Variances

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

• Suparat Niwitpong

• Confidence interval
• generalized confidence interval
• the closed form method of variance estimation
• variance.

[1] A. Donner, GY. Zou, Closed-form confidence intervals for function of
the normal mean and standard deviation, Statistical Methods in Medical
Research, (2010) 1-12.
[2] GY. Zou, CY. Huo, J. Taleban, Simple confidence intervals for lognormal
means and their differences with environmental applications, Environmetrics
20 (2009) 172-180.
[3] GY. Zou, J. Taleban, C. Huo, Confidence interval estima tion for lognormal
data with application to health economics, Computational Statistics
and Data Analysis, 53 (2009) 3755-3764.
[4] GY. Zou, A. Donner, A simple alternative confidence interval for the
difference between two proportions, Controlled Clinical Trials 25 (2004)
3-12.
[5] GY. Zou, W. Huang, X. Zhang, A note on confidence interval estimation
for a linear function of binomial proportions, Computational Statistics
and Data Analysis, 53 (2009) 1080-1085.
[6] K. Krishnamoorthy, T. Mathew, Inferences on the means of lognormal
distributions using generalized p-values and generalized confidence intervals,
Journal of Statistical Planning and Inference, 115 (2003)103-120.
[7] K. Krishnamoorthya, Y. Lina, Y. Xia, Confidence limits and prediction
limits for a Weibull distribution based on the generalized variable approach,
Journal of Statistical Planning and Inference, 139 (2009) 2675 -
2684
[8] L. Tian, Interval estimation and hypothesis testing of intraclass correlation
coeffcients: the generalized variable approach, Statistical in medicine, 24
(2005) 1745-1753.
[9] RD. Herbert, A. Hayen, P. Macaskill, SD. Walter, Interval estimation
for the difference of two independent variances, Communications in
StatisticsSimulation and Computation, 40 (2011) 744-758.
[10] S. Weerahandi, Generalized confidence intervals, The Journal of American
Statistical Association, 88 (1993) 899-905.
[11] The R Development Core Team, An Introduction to R, Vienna: R
Foundation for Statistical Computing, http://www.R-project.org, 2010.
[12] V. Cojbasica, A. Tomovica, Nonparametric confidence intervals for
population variance of one sample and the diffeence of variances of two
samples, Computational Statistics & Data Analysis, 51 (2007) 5562-5578.