CoefVarCI: R6 Confidence Intervals for the Coefficient of Variation (cv)

In cvcqv: Coefficient of Variation (CV) with Confidence Intervals (CI)

R6 Confidence Intervals for the Coefficient of Variation (cv)

Description

The R6 class CoefVarCI for the confidence intervals of coefficient of variation (cv)

Arguments

x	An R object. Currently there are methods for numeric vectors
na.rm	a logical value indicating whether NA values should be stripped before the computation proceeds.
digits	integer indicating the number of decimal places to be used.
method	a scalar representing the type of confidence intervals required. The value should be any of the values "kelley_ci", "mckay_ci", "miller_ci", "vangel_ci", "mahmoudvand_hassani_ci", "equal_tailed_ci", "shortest_length_ci", "normal_approximation_ci", "norm_ci","basic_ci", "aak_adj_ci", "aak_ls_ci", "aak_als_ci", or "all_ci".
alpha	The allowed type I error probability
R	integer indicating the number of bootstrap replicates.
correction	returns the unbiased estimate of the coefficient of variation if TRUE is determined.

Details

Coefficient of Variation

The cv is a measure of relative dispersion representing the degree of variability relative to the mean [1]. Since cv is unitless, it is useful for comparison of variables with different units. It is also a measure of homogeneity [1].

Value

An object of type "list" which contains the estimate, the intervals, and the computation method. It has two main components:

$method

A description of statistical method used for the computations.

$statistics

A data frame representing three vectors: est/, lower and upper limits of confidence interval (CI); additional description vector is provided when "all" is selected:

est: cv*100

Kelley Confidence Interval: Thanks to package MBESS [2] for the computation of confidence limits for the noncentrality parameter from a t distribution conf.limits.nct [3].

McKay Confidence Interval: The intervals calculated by the method introduced by McKay [4], using chi-square distribution.

Miller Confidence Interval: The intervals calculated by the method introduced by Miller [5], using the standard normal distribution.

Vangel Confidence Interval: Vangel [6] proposed a method for the calculation of CI for cv; which is a modification on McKay’s CI.

Mahmoudvand-Hassani Confidence Interval: Mahmoudvand and Hassani [7] proposed a new CI for cv; which is obtained using ranked set sampling (RSS)

Normal Approximation Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is a normal approximation.

Shortest-Length Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is obtained through minimizing the length of CI.

Equal-Tailed Confidence Interval: Wararit Panichkitkosolkul [8] proposed another CI for cv; which is obtained using chi-square distribution.

Bootstrap Confidence Intervals: Thanks to package boot by Canty & Ripley [9] we can obtain bootstrap CI around cv using boot.ci.

Abu-Shawiesh-Akyuz-Kibria Confidence Intervals: Abu-Shawiesh, Akyuz, & Kibria [10] proposed three CIs for the population cv that adjust for non-normality through the sample kurtosis: the adjusted-degrees-of-freedom CI (aak_adj_ci) derived from Hummel et al.'s CI for the variance, the large-sample CI (aak_ls_ci) derived from the log-transformed CI for the variance, and the augmented-large-sample CI (aak_als_ci) derived from Burch's CI for the variance.

References

[1] Albatineh, AN., Kibria, BM., Wilcox, ML., & Zogheib, B, 2014, Confidence interval estimation for the population coefficient of variation using ranked set sampling: A simulation study, Journal of Applied Statistics, 41(4), 733–751, DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/02664763.2013.847405")}

[2] Kelley, K., 2018, MBESS: The MBESS R Package. R package version 4.4. 3.

[3] Kelley, K., 2007, Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach, Behavior Research Methods, 39(4), 755–766, DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3758/BF03192966")}

[4] McKay, AT., 1932, Distribution of the Coefficient of Variation and the Extended“ t” Distribution, Journal of the Royal Statistical Society, 95(4), 695–698

[5] Miller, E., 1991, Asymptotic test statistics for coefficients of variation, Communications in Statistics-Theory and Methods, 20(10), 3351–3363

[6] Vangel, MG., 1996, Confidence intervals for a normal coefficient of variation, The American Statistician, 50(1), 21–26

[7] Mahmoudvand, R., & Hassani, H., 2009, Two new confidence intervals for the coefficient of variation in a normal distribution, Journal of Applied Statistics, 36(4), 429–442

[8] Panichkitkosolkul, W., 2013, Confidence Intervals for the Coefficient of Variation in a Normal Distribution with a Known Population Mean, Journal of Probability and Statistics, 2013, 1–11, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1155/2013/324940")}

[9] Canty, A., & Ripley, B., 2017, boot: Bootstrap R (S-Plus) Functions, R package version 1.3-20

[10] Abu-Shawiesh, MOA., Akyuz, HE., & Kibria, BG., 2019, Performance of Some Confidence Intervals for Estimating the Population Coefficient of Variation under both Symmetric and Skewed Distributions, Statistics, Optimization & Information Computing, 7(2), 277-290, DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.19139/soic.v7i2.630")}

Examples

y <- c(
    0.2, 0.5, 1.1, 1.4, 1.8, 2.3, 2.5, 2.7, 3.5, 4.4,
    4.6, 5.4, 5.4, 5.7, 5.8, 5.9, 6.0, 6.6, 7.1, 7.9
)
CoefVarCI$new(x = y)$kelley_ci()
cv_y <- CoefVarCI$new(
   x = y,
   alpha = 0.05,
   R = 1000,
   digits = 2,
   correction = TRUE
)
cv_y$kelley_ci()
cv_y$mckay_ci()
R6::is.R6(cv_y)

cvcqv documentation built on July 6, 2026, 5:07 p.m.