# Read me code for 
# "Multivariate coefficients of variation: comparison and influence functions"
# Aerts Stphanie, Haesbroeck Gentiane and Ruwet Christel

In this folder, there are main and auxiliary R files.

Main files:
	- "MCV_consist.R" : functions ('MCV' and 'uniCV') to compute consistent multivariate coefficient of variation estimates.
				The considered MCV are Reyment's, Van Valen's, Voinov & Nikulin's and Albert & Zhang's
				The considered estimators are the classical, MCD, RMCD and S estimators for (p>1) and IQRmed and MADmed for (p=1).
				The considered distributions are the multivariate normal, Student and Power exponential distributions.

	- "DiagnosticTool.R" : function ('DiagTool') to compute the diagnostic tool to detect influential observations and the associated plots.
				The considered MCV are Reyment's, and Voinov & Nikulin's
				The considered estimators are the classical, MCD, RMCD and S estimators. 
				The considered distribution is the multivariate normal.

	- "ASVnormality.R" : functions ('ASV_Reyment' and 'ASV_VN') to compute the asymptotic variances of Reyment and Voinov and Nikulin's estimates 
				The considered MCV are Reyment's and Voinov & Nikulin's
				The considered estimators are the classical, MCD, and S estimators. 
				The considered distribution is the multivariate normal
					NB: the computation of these ASVs for Voinov & Nikulin's under more general conditions 
					(Student and Power exponential) and for more estimates can be found in the code related to the paper :
					"Distribution under elliptical symmetry of a distance-based multivariate coefficient of variation"

Auxiliary files:
	- "MCDconsist.R" 	: function ('consistMCD') to compute the MCD and RMCD consistent location and scatter estimators
	- "Sconsist.R"		: function ('consistS') to compute the S consistent location and scatter estimators
	- "fastS_consistency.R"	: additional function ('fastSmulti_location') to compute the consistent location and scatter estimators
	- "fastS_normality.R"	: additional function ('fastSmulti_consist') to compute the consistent location and scatter estimators under normality


	

