The entropic log odds as a measure of distribution asymmetry

The entropic measure of distributional spread, representing the total binary code complexity of the probability distribution, is equal to the area under the partition entropy function. A conjugate dual, obtained as a simple internal sign change from the partition entropy function, can be employed to indicate the relative complexity to the right of any given point versus that to the left. The area beneath this function constitutes a dual measure of distribution asymmetry, which can be reconciled with one based on conditional expected values.