The bounds of the concentration index when the variable of interest is binary, with an application to immunization inequality

When the health sector variable whose inequality is being investigated is binary, the minimum and maximum possible values of the concentration index are equal to micro-1 and 1-micro, respectively, where micro is the mean of the variable in question. Thus as the mean increases, the range of the possible values of the concentration index shrinks, tending to zero as the mean tends to one and the concentration index tends to zero. Examples are...