Concentration of Distributions at Entropy Maxima (1979)

Abstract

After sending off the ‘Where Do We Stand?’ manuscript for the MIT Proceedings Volume, my thoughts returned to Rudolph Wolf’s dice data. The hastily concocted argument for five degree of freedom instead of three bothered me a bit, and I decided to calculate how much Chi-squared could have been reduced if the parameters λ₁, λ₂ bad been chosen to minimize it, rather than from the Maxent rule. But first, as a check on the old computer program, I recalculated the entropies of those various distributions. Quite by accident, I noticed that the numerical values of NΔH were in every case just half the values of Chi-squared in the MIT article.