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The value of a characteristic function of a random variable X at some real number t is the center of mass of the distribution of tX wrapped around the unit circle in the complex plane. This geometrical representation is used to illustrate how various properties of frequency functions and characteristic functions correspond and to illuminate the role of empirical characteristic functions in statistical inference.doi:10.2307/2684780 fatcat:twsab6oquvhyfck2tf45bp76ea