Editing Coefficient of variation (section)

=== As a measure of economic inequality ===

The coefficient of variation fulfills the [[Income inequality metrics|requirements for a measure of economic inequality]].<ref name="Champ1999">{{cite book |last1=Champernowne |first1=D. G.|last2=Cowell |first2=F. A.|date=1999 |title=Economic Inequality and Income Distribution |publisher=Cambridge University Press }}</ref><ref name="Campano2006">{{cite book |last1=Campano |first1=F. |last2=Salvatore |first2=D. |date=2006 |title=Income distribution |publisher=Oxford University Press }}</ref><ref name="Bellu2006">{{cite web |url=http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf |title=Policy Impacts on Inequality – Simple Inequality Measures |last1=Bellu |first1=Lorenzo Giovanni |last2=Liberati |first2=Paolo |date=2006 |website=EASYPol, Analytical tools |publisher=Policy Support Service, Policy Assistance Division, FAO |access-date=13 June 2016 |url-status=live |archive-url=https://web.archive.org/web/20160805101141/http://www.fao.org/docs/up/easypol/448/simple_inequality_mesures_080en.pdf |archive-date=5 August 2016 |df=dmy-all }}</ref> If '''x''' (with entries ''x''<sub>''i''</sub>) is a list of the values of an economic indicator (e.g. wealth), with ''x''<sub>''i''</sub> being the wealth of agent ''i'', then the following requirements are met:

* Anonymity – ''c''<sub>''v''</sub> is independent of the ordering of the list '''x'''. This follows from the fact that the variance and mean are independent of the ordering of '''x'''.
* Scale invariance: ''c''<sub>v</sub>('''x''') = ''c''<sub>v</sub>(&alpha;'''x''') where ''&alpha;'' is a real number.<ref name="Bellu2006" />
* Population independence – If {'''x''','''x'''} is the list '''x''' appended to itself, then ''c''<sub>''v''</sub>({'''x''','''x'''}) = ''c''<sub>''v''</sub>('''x'''). This follows from the fact that the variance and mean both obey this principle.
* Pigou–Dalton transfer principle: when wealth is transferred from a wealthier agent ''i'' to a poorer agent ''j'' (i.e. ''x''<sub>''i''</sub>&nbsp;>&nbsp;''x''<sub>''j''</sub>) without altering their rank, then ''c''<sub>''v''</sub> decreases and vice versa.<ref name="Bellu2006" />

''c''<sub>''v''</sub> assumes its minimum value of zero for complete equality (all ''x''<sub>''i''</sub> are equal).<ref name="Bellu2006" /> Its most notable drawback is that it is not bounded from above, so it cannot be normalized to be within a fixed range (e.g. like the [[Gini coefficient]] which is constrained to be between 0 and 1).<ref name="Bellu2006" /> It is, however, more mathematically tractable than the Gini coefficient.