README.md

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

cvcqv

cvcqv provides some easy-to-use functions and classes to calculate Coefficient of Variation (cv) and Coefficient of Quartile Variation (cqv) with confidence intervals provided with all available methods.

Overview

Background

There are abundant methods available for the calculation of confidence intervals of a dispersion measure like coefficient of variation (cv) or coefficient of quartile variation (cqv), which have not yet been implemented in R. Also, cqv is quite useful in conditions where the distribution of variables does not follow normal distribution.

Coefficient of Variation

cv is a measure of relative dispersion representing the degree of variability relative to the mean (Albatineh et al, 2014). Since cv is unitless, it is useful for comparison of variables with different units. It is also a measure of homogeneity (Albatineh et al, 2014).

Coefficient of Quartile Variation

cqv is a measure of relative dispersion that is based on interquartile range (IQR). Since cqv is unitless, it is also useful for comparison of variables with different units. It is also a measure of homogeneity (Bonett, 2006; Altunkaynak, 2018).

Confidence Interval

Since the measurements of cv and cqv are obtained from samples, we cannot easily generalize them and decide based upon them. Confidence Intervals (CI) help us to make a probabilistic interval around the estimation of calculated cv and cqv. For example, 95% CI indicates that it is 95% probable that the measurement for a population lies between the lower and upper bounds of that CI.

Installation

If you are an ubuntu user, you are going to need these non-R packages:

sudo apt install libcurl4-openssl-dev libssl-dev libxml2-dev libgsl-dev   

The cvcqv package is available on CRAN. To install:

install.packages("cvcqv")

The cvcqv package is also available on github. To install it in R, use:

devtools::install_github('MaaniBeigy/cvcqv')  

* Currently, these tools are available:

| name | is.R6.. | Description | |:-----------------|:--------|:----------------------------------------| | CoefVar | TRUE | Coefficient of Variation (cv) | | CoefQuartVar | TRUE | Coefficient of Quartile Variation (cqv) | | CoefVarCI | TRUE | Confidence Intervals for cv | | CoefQuartVarCI | TRUE | Confidence Intervals for cqv | | SampleQuantiles | TRUE | Sample Quantiles | | cv_versatile | FALSE | Coefficient of Variation | | cqv_versatile | FALSE | Coefficient of Quartile Variation | | BootCoefVar | TRUE | Bootstrap Resampling for cv | | BootCoefQuartVar | TRUE | Bootstrap Resampling for cqv |

* This package is inspired by dplyr, R6, SciView, boot, and MBESS.

Example

Here, we want to observe all available confidence intervals for the cv of variable x:

x <- 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
)
results <- CoefVarCI$new(x, digits = 3)$all_ci()  # R6 class
# or alternatively: 
results <- cv_versatile(x, digits = 3, method = "all")  # functional programming

The results will be:

| | est | lower | upper | description | |:---|---:|---:|---:|:---| | kelley | 57.774 | 41.287 | 97.894 | cv with Kelley 95% CI | | mckay | 57.774 | 41.441 | 108.483 | cv with McKay 95% CI | | miller | 57.774 | 34.053 | 81.495 | cv with Miller 95% CI | | vangel | 57.774 | 41.264 | 105.426 | cv with Vangel 95% CI | | mahmoudvand_hassani | 57.774 | 43.476 | 82.857 | cv with Mahmoudvand-Hassani 95% CI | | equal_tailed | 57.774 | 43.937 | 84.383 | cv with Equal-Tailed 95% CI | | shortest_length | 57.774 | 42.015 | 81.013 | cv with Shortest-Length 95% CI | | normal_approximation | 57.774 | 44.533 | 85.272 | cv with Normal Approximation 95% CI | | norm | 57.774 | 38.799 | 78.937 | cv with Normal Approximation Bootstrap 95% CI | | basic | 57.774 | 35.055 | 78.167 | cv with Basic Bootstrap 95% CI | | perc | 57.774 | 38.879 | 79.174 | cv with Bootstrap Percentile 95% CI | | bca | 57.774 | 40.807 | 82.297 | cv with Adjusted Bootstrap Percentile (BCa) 95% CI | | aak_adj | 57.774 | 48.029 | 72.516 | cv with Abu-Shawiesh-Akyuz-Kibria ADJ 95% CI | | aak_ls | 57.774 | 46.310 | 72.075 | cv with Abu-Shawiesh-Akyuz-Kibria LS 95% CI | | aak_als | 57.774 | 45.839 | 75.092 | cv with Abu-Shawiesh-Akyuz-Kibria ALS 95% CI |

Next, we want to find all of the available confidence intervals for the cqv of variable x:

results <- CoefQuartVarCI$new(x, digits = 3)$all_ci()  # R6 class
# or alternatively:
results <- cqv_versatile(x, , digits = 3, method = "all")  # functional programming

The results will be:

| | est | lower | upper | description | |:--------|-------:|-------:|-------:|:------------------------------------------------| | bonett | 45.625 | 24.785 | 77.329 | cqv with Bonett CI | | norm | 45.625 | 19.957 | 70.840 | cqv with normal approximation CI | | basic | 45.625 | 18.992 | 73.917 | cqv with basic bootstrap CI | | percent | 45.625 | 17.122 | 68.683 | cqv with bootstrap percentile CI | | bca | 45.625 | 24.273 | 83.264 | cqv with adjusted bootstrap percentile (BCa) CI |

Documentation

Once installed, browse the package vignettes:

browseVignettes("cvcqv")

References

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: https://doi.org/10.1080/02664763.2013.847405

Bonett, DG., 2006, Confidence interval for a coefficient of quartile variation, Computational Statistics & Data Analysis, 50(11), 2953-7, DOI: https://doi.org/10.1016/j.csda.2005.05.007

Altunkaynak, B., Gamgam, H., 2018, Bootstrap confidence intervals for the coefficient of quartile variation, Simulation and Computation, 1-9, DOI: https://doi.org/10.1080/03610918.2018.1435800

Abu-Shawiesh, M. O. A., Akyuz, H. E., & Kibria, B. M. G., 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: https://doi.org/10.19139/soic.v7i2.630

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