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.
Aims
The authors' intention is to create a small R package adhering to K-I-S-S principle to facilitate the use of the most available rigorous methods for calculation of confidence intervals around the variability measures of cv and cqv.
Convention
We are bound by the high standards of functional programming (FP) and object-oriented programming (OOP). The majority of tools provided by cvcqv are developed as both FP tools and R6 classes, for sake of versatility, portability and efficiency.
Getting started
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 is 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.
Examples
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 programmingThe 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 |
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
Download the cvcqv_1.0.0.tar.gz. Install the source package cvcqv from the Packages >> Install >> Package Archive File (.tar.gz) >> Browse >> cvcqv_1.0.0.tar.gz. Or run an installation code like:
install.packages("~/cvcqv_1.0.0.tar.gz", repos = NULL, type = "source")Then, browse for vignettes:
browseVignettes("cvcqv")Then, select html to show the vignette.
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: http://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: http://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: http://doi.org/10.1080/03610918.2018.1435800
