Abstract
This article considers inference for a common coefficient of variation (CV) shared by several normal populations. The confidence distributions (CD) are used to combine the information about each CV from different sources. A new procedure for constructing a confidence interval for the common CV is developed based on a combined confidence distribution for the inverse of the CV. The new derived CD interval has a theoretical exact frequentist property. Simulation results demonstrate that the new confidence intervals perform very well in terms of empirical coverage probability and average interval length. Finally, the proposed new procedure is illustrated on a real data example.
Highlights
The coefficient of variation (CV) of a distribution is defined to be the ratio of the standard deviation σ to the mean μ, i.e., η = σ μThis parameter is a useful measure of dispersion because it is not affected by the units of measurement, and it has many applications in different scientific fields
[28], Verrill and Johnson [30], Forkman [9], Liu et al [18], and Krishnamoorthy and Lee [15], etc. Among these works, Ahmed [1], Tian [28] and Forkman [9] considered the problem of estimating the coefficients of variance (CsV) when it is apriori suspected that several CsV are the same
We propose a new interval estimation procedure for a common CV shared by several normal populations using a confidence distribution (CD) and combined CD approach
Summary
The coefficient of variation (CV) of a distribution is defined to be the ratio of the standard deviation σ to the mean μ, i.e., η. Xu [28], Verrill and Johnson [30], Forkman [9], Liu et al [18], and Krishnamoorthy and Lee [15], etc Among these works, Ahmed [1], Tian [28] and Forkman [9] considered the problem of estimating the coefficients of variance (CsV) when it is apriori suspected that several CsV are the same. We are interested in the problem just mentioned above, that is, investigating how to pool the information about a common CV from different populations and give confidence intervals for it For this purpose, we will use a confidence distribution (CD) as a main tool, take advantage of its good property for combining information and derive a new confidence interval based on a combined CD for the common inverse of the CV.
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