Title: Confidence Interval for Standard Deviation of Normal Distribution with Known Coefficients of Variation
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:...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. Recently, Herbert et al. (2) have argued that methods and analyzes for constructing the confidence interval estimation of the difference between variances have not been described. They proposed a simple analytical method to construct a confidence interval for the difference between two independent samples. It is seen that their proposed confidence interval works well when observations are highly skewed and leptokurtic. Cojbasica and Tomovica (1) showed that the nonparametric confidence interval of the population variance of two-sample problem based on t-statistic combined with bootstrap techniques performs very well when data are from exponential families. Phonyiem and Niwitpong (5) proposed the new generalized confidence interval for the difference between the normal variances.Their proposed interval performs very well compared to the existing confidence interval. Related works of the confidence interval for the difference between two variances, the reader is referred to the references cited in the above papers. In this paper, we emphasize only data are from the normal distribution and we propose the new confidence interval for the single and the difference of two normal population standard deviations, based on the simple confidence interval of (3). For the confidence interval for a standard deviation, we derived analytic expressions to find coverage probability and expected length. We also present the Monte Carlo simulation results for the confidence intervals for the difference of standard deviations.Read More
Publication Year: 2015
Publication Date: 2015-01-25
Language: en
Type: article
Indexed In: ['crossref']
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