PyMaxEnt is a python software that solves the inverse moment problem using the maximum entropy principle. Given a finite number of moments, PyMaxEnt will find the function that generates those moments and also maximizes the information entropy.
To use PyMaxEnt, a single function call to reconstruct(moments, ivars, bnds, scaling) is made. Here, moments is a required list or array of known moments, ivars is an optional argument containing discrete values of the independent variable, bnds is a tuple [a,b] containing the expected bounds of the resulting distribution, and scaling is the invariant measure or the scaling function.
When ivars is provided, the reconstruction assumes a discrete distribution. When a discrete reconstruction is chosen, scaling should be an array of the same size as ivars.
More details can be found in src/pymaxent.py.
Below are some examples of using the \MaxEnt software. Starting with an example to reconstruct a basic dicrete distribution with two moments and four independent variables
from pymaxent import *
mu = [1,3.5]
x = [1,2,3,4,5,6]
sol, lambdas = reconstruct(mu,ivars=x)Similarly, for a continuous distribution, one passes a list of input moments.
In this case, however, one must specify the bounds (bnds) to indicate that this is a continuous reconstruction.
Here's an example for a Gaussian distribution
from pymaxent import *
mu = [1,0,0.04]
sol, lambdas = reconstruct(mu,bnds=[-1,1])
# plot the reconstructed solution
x = np.linspace(-1,1)
plot(x,sol(x))