Compute the coefficient of variation (CV, ratio of the standard deviation to the mean, \(\sigma/\mu\)) for a set of numeric values.

## Usage

```
coef_var(x, ...)
distribution_coef_var(x, ...)
# S3 method for numeric
coef_var(
x,
mu = NULL,
sigma = NULL,
method = c("standard", "unbiased", "median_mad", "qcd"),
trim = 0,
na.rm = FALSE,
n = NULL,
...
)
```

## Arguments

- x
A numeric vector of ratio scale (see details), or vector of values than can be coerced to one.

- ...
Further arguments passed to computation functions.

- mu
A numeric vector of mean values to use to compute the coefficient of variation. If supplied,

`x`

is not used to compute the mean.- sigma
A numeric vector of standard deviation values to use to compute the coefficient of variation. If supplied,

`x`

is not used to compute the SD.- method
Method to use to compute the CV. Can be

`"standard"`

to compute by dividing the standard deviation by the mean,`"unbiased"`

for the unbiased estimator for normally distributed data, or one of two robust alternatives:`"median_mad"`

to divide the median by the`stats::mad()`

, or`"qcd"`

(quartile coefficient of dispersion, interquartile range divided by the sum of the quartiles [twice the midhinge]: \((Q_3 - Q_1)/(Q_3 + Q_1)\).- trim
the fraction (0 to 0.5) of values to be trimmed from each end of

`x`

before the mean and standard deviation (or other measures) are computed. Values of`trim`

outside the range of (0 to 0.5) are taken as the nearest endpoint.- na.rm
Logical. Should

`NA`

values be removed before computing (`TRUE`

) or not (`FALSE`

, default)?- n
If

`method = "unbiased"`

and both`mu`

and`sigma`

are provided (not computed from`x`

), what sample size to use to adjust the computed CV for small-sample bias?

## Details

CV is only applicable of values taken on a ratio scale: values that have a
*fixed* meaningfully defined 0 (which is either the lowest or highest
possible value), and that ratios between them are interpretable For example,
how many sandwiches have I eaten this week? 0 means "none" and 20 sandwiches
is 4 times more than 5 sandwiches. If I were to center the number of
sandwiches, it will no longer be on a ratio scale (0 is no "none" it is the
mean, and the ratio between 4 and -2 is not meaningful). Scaling a ratio
scale still results in a ratio scale. So I can re define "how many half
sandwiches did I eat this week ( = sandwiches * 0.5) and 0 would still mean
"none", and 20 half-sandwiches is still 4 times more than 5 half-sandwiches.

This means that CV is **NOT** invariant to shifting, but it is to scaling: