%0 Journal Article
%T Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean
%A Wararit Panichkitkosolkul
%J Journal of Probability and Statistics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/324940
%X This paper presents three confidence intervals for the coefficient of variation in a normal distribution with a known population mean. One of the proposed confidence intervals is based on the normal approximation. The other proposed confidence intervals are the shortest-length confidence interval and the equal-tailed confidence interval. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence intervals with the existing confidence intervals. Simulation results have shown that all three proposed confidence intervals perform well in terms of coverage probability and expected length. 1. Introduction The coefficient of variation of a distribution is a dimensionless number that quantifies the degree of variability relative to the mean [1]. It is a statistical measure for comparing the dispersion of several variables obtained by different units. The population coefficient of variation is defined as a ratio of the population standard deviation to the population mean given by . The typical sample estimate of is given as where is the sample standard deviation, the square root of the unbiased estimator of population variance, and is the sample mean. The coefficient of variation has been widely used in many areas such as science, medicine, engineering, economics, and others. For example, the coefficient of variation has also been employed by Ahn [2] to analyze the uncertainty of fault trees. Gong and Li [3] assessed the strength of ceramics by using the coefficient of variation. Faber and Korn [4] applied the coefficient of variation as a way of including a measure of variation in the mean synaptic response of the central nervous system. The coefficient of variation has also been used to assess the homogeneity of bone test samples to help determine the effect of external treatments on the properties of bones [5]. Billings et al. [6] used the coefficient of variation to study the impact of socioeconomic status on hospital use in New York City. In finance and actuarial science, the coefficient of variation can be used as a measure of relative risk and a test of the equality of the coefficients of variation for two stocks [7]. Furthermore, Pyne et al. [8] studied the variability of the competitive performance of Olympic swimmers by using the coefficient of variation. Although the point estimator of the population coefficient of variation shown in (1) can be a useful statistical measure, its confidence interval is more useful than the point estimator. A confidence interval provides much more information about the population
%U http://www.hindawi.com/journals/jps/2013/324940/