Distance correlation, covariance and correlation statistics.
It returns distace correlation (dCor), distance covariance (dCov), diatance variace on x (dVarX) and distance variance on y (dVarY).
Reference: https://en.wikipedia.org/wiki/Distance_correlation
See also: corr, cov.
The following code
base=@(x) (x- min(x))./(max(x)-min(x)); N = 5e2; x = randn (N,1); x = base (x); z = randn (N,1); z = base (z); # Linear relations cy = [1 0.55 0.3 0 -0.3 -0.55 -1]; ly = x .* cy; ly(:,[1:3 5:end]) = base (ly(:,[1:3 5:end])); # Correlated Gaussian cz = 1 - abs (cy); gy = base ( ly + cz.*z); # Shapes sx = repmat (x,1,7); sy = zeros (size (ly)); v = 2 * rand (size(x,1),2) - 1; sx(:,1) = v(:,1); sy(:,1) = cos(2*pi*sx(:,1)) + 0.5*v(:,2).*exp(-sx(:,1).^2/0.5); R =@(d) [cosd(d) sind(d); -sind(d) cosd(d)]; tmp = R(35) * v.'; sx(:,2) = tmp(1,:); sy(:,2) = tmp(2,:); tmp = R(45) * v.'; sx(:,3) = tmp(1,:); sy(:,3) = tmp(2,:); sx(:,4) = v(:,1); sy(:,4) = sx(:,4).^2 + 0.5*v(:,2); sx(:,5) = v(:,1); sy(:,5) = 3*sign(v(:,2)).*(sx(:,5)).^2 + v(:,2); sx(:,6) = cos (2*pi*v(:,1)) + 0.5*(x-0.5); sy(:,6) = sin (2*pi*v(:,1)) + 0.5*(z-0.5); sx(:,7) = x + sign(v(:,1)); sy(:,7) = z + sign(v(:,2)); sy = base (sy); sx = base (sx); # scaled shape sc = 1/3; ssy = (sy-0.5) * sc + 0.5; n = size (ly,2); ym = 1.2; xm = 0.5; fmt={'horizontalalignment','center'}; ff = "% .2f"; figure (1) for i=1:n subplot(4,n,i); plot (x, gy(:,i), '.b'); axis tight axis off text (xm,ym,sprintf (ff, dcov (x,gy(:,i))),fmt{:}) subplot(4,n,i+n); plot (x, ly(:,i), '.b'); axis tight axis off text (xm,ym,sprintf (ff, dcov (x,ly(:,i))),fmt{:}) subplot(4,n,i+2*n); plot (sx(:,i), sy(:,i), '.b'); axis tight axis off text (xm,ym,sprintf (ff, dcov (sx(:,i),sy(:,i))),fmt{:}) v = axis (); subplot(4,n,i+3*n); plot (sx(:,i), ssy(:,i), '.b'); axis (v) axis off text (xm,ym,sprintf (ff, dcov (sx(:,i),ssy(:,i))),fmt{:}) endfor
Produces the following figure
Figure 1 |
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Package: statistics