This book is the culmination of roughly seven years of joint research be tween us. We have both been interested in income inequality measurement for a considerably longer period of time. One author (Ryu) has a back ground in physics. While he was working on his Ph. D. in Physics at M. I. T. he became acquainted with Robert Solow. Professor Solow introduced Ryu to economics. After finishing his Ph. D. in physics, Ryu went on to the Uni versity of Chicago where Arnold Zellner guided him to a dissertation on using orthonormal basis and maximum entropy as estimation methods in econometric...