Continuous MaxEnt Distributions in Mathematica: a "Parameter-Free" Approach

Mathematica is used to develops a method of obtaining continuous MaxEnt distributions using the Lagrange Multiplier method that works directly in the discrete case. The continuous PDF (probability density function) is described by list of coordinates of the form {{abs(1), ord(1)}, {abs(2), ord(2)}, ... , {abs(n), ord(n)}}, where the abscissae abs(i) are specified numerically so as to define the domain of the PDF, and the ordinates ord(i) are initially general symbolic variables that are assigned numeric values via the procedure to be described. In all the applications given here, n=51. A set of Lagrange Multiplier equations is solved for the ordi, making use of the fact that the Mathematica function Interpolation[], which constructs interpolationFunction objects normally used for numeric data and for describing numerical solutions to differential equations, can operate on "semi-symbolic" data.