Is there a non-parametric Coefficient of Variation? I was reading a paper where the author mentions: "The coefficient of variation is primarily a descriptive statistic, but it is amenable to statistical inferences such as null hypothesis testing or confidence intervals. Standard procedures are often very dependent of the normality assumption and current work is exploring alternative procedures which are less dependent on this normality assumption."
The paper is from 2010. So my question is: has there been any recent "advancements" in terms of a coefficient of variation statistic that is not dependent upon the normality assumption? And, is this what one may call a non-parametric CV?
 A: The coefficient of variation is not strongly associated with the normal distribution at all. It is most obviously pertinent for distributions like the lognormal or gamma. See e.g. this thread. 
Looking at ratios such as interquartile range/median is possible. In many situations that ratio might be more resistant to extreme values than the coefficient of variation. The measure seems neither common nor especially useful, but it certainly predates 2010. Tastes vary, but I see no reason to call that ratio nonparametric; it just uses different parameters. 
A much better developed approach is to use the ratio of the second and first $L$-moment. The first $L$-moment is just the mean, but the second $L$-moment has more resistance than the standard deviation. Start (e.g.) here for more on $L$-moments. 
Whenever the coefficient of variation seems natural, that's usually a sign that analyses should be conducted on a logarithmic scale. If CV is (approximately) constant, then SD is proportional to the mean, which goes with comparisons and changes being multiplicative rather than additive, which implies thinking logarithmically. 
Note: The paper cited starts quite well, but then focuses on testing the CV when the distribution is normal. As above, if the distribution is normal, then the CV seems utterly uninteresting in practice, so the emphasis is puzzling to me. Your inclinations may differ. 
A: The coefficient of variation $\sigma / \mu$ itself has no normality assumption - just that the first two moments of the distribution are computable.  I think it's a nonparametric test for the CV that you're looking for.
Googling "nonparametric coefficient of variation test" turned up a variety of papers on tests, depending on what kind of test you might be interested in.  Ex:


*

*Nonparametric tests for a change in the coefficient of variation

*Nonparametric Tests for Comparing Several Coefficients of Variation
