Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation

Suparat Niwitpong

doi:https://doi.org/10.14445/22315373/IJMTT-V17P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 17 | Number 2 | Year 2015 | Article Id. IJMTT-V17P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V17P515

Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation

Suparat Niwitpong

Abstract

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, the new confidence interval for the difference between two normal population standard deviations based on the simple confidence interval of Donner and Zou [Closed-form confidence intervals for functions of the normal mean and standard deviation, 1-13, 2010.]. For a single confidence interval for a standard deviation, we derived analytic expressions to find the coverage probability and its expected length compared with the standard confidence interval. Monte Carlo simulation results for the difference of standard deviations are given to compare proposed confidence intervals.

Keywords

Coverage probability, Expected length, Variances

References

[1] V. Cojbasica, A. Tomovica, “Nonparametric confidence Intervals for population variance of one sample and the difference of variances of two samples,” Computational Statistics & Data Analysis, vol. 51, pp. 5562-5578, 2007.
[2] R.D. Herbert, P. Hayen, P. Macaskill, SD. Walter, “ Interval estimation for the difference of two independent variances,” Communications in Statistics: Simulation and Computation , vol. 40, pp. 744-758, 2011.
[3] A. Donner, G.Y. Zou, “Closed-form confidence intervals for functions of the normal mean and standard deviation,” Stat Methods Med Res, pp. 1-13, 2010.
[4] S. Niwitpong, S. Niwitpong, “Confidence interval for the difference oftwo normal population means with a known ratio of variances,” Applied Mathematical Sciences, vol. 4, pp. 347 – 359, 2010.
[5] W. Phonyiem, S. Niwitpong, “Generalized confidence interval For the difference between normal population variances,” Far East Journal of Mathematical Sciences, vol. 69, pp. 99-110, 2012.

Citation :

Suparat Niwitpong, "Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 17, no. 2, pp. 111-118, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V17P515