function f = distance(inverse_uncertainty_distribution_1,inverse_uncertainty_distribution_2)
iud = @(alpha)inverse_uncertainty_distribution_1(alpha)-inverse_uncertainty_distribution_2(1-alpha);

small = 0.0000001;
if iud(1-small)<0 
    Phi0 = 1-small;
elseif iud(small)>0
    Phi0 = small;
else b = 0; t = 1; 
     while t-b>small
         c = (b+t)./2;
         if iud(c) < 0
          b=c;
         else t=c;
         end
     end
     Phi0 = (b+t)./2;
end
f = quadl(iud,Phi0,1-small)-quadl(iud,small,Phi0);
end