Compute Discrete Maximum Entropy Distributions
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The maximum entropy method, or MAXENT, is variational approach for computing probability distributions given a list of moment, or expected value, constraints.

Here are some links for background info. A good overview of applications: On the idea of maximum entropy in general:

Use this package to compute discrete maximum entropy distributions over a list of values and list of constraints.

Here is a the example from Probability the Logic of Science

maxent ([1,2,3], [average 1.5])

Right [0.61, 0.26, 0.11]

The classic dice example

maxent ([1,2,3,4,5,6], [average 4.5])

Right [.05, .07, 0.11, 0.16, 0.23, 0.34]

One can use different constraints besides the average value there.

As for why you want to maximize the entropy to find the probability constraint, I will say this for now. In the case of the average constraint it is a kin to choosing a integer partition with the most interger compositions. I doubt that makes any sense, but I will try to explain more with a blog post soon.