A Matlab Program to Calculate the Maximum Entropy Distributions

TL;DR

This paper provides three Matlab programs to compute maximum entropy distributions for general, power, and Fourier series functions, aiding researchers in solving related inverse problems efficiently.

Contribution

It introduces specific Matlab implementations for calculating Lagrange multipliers in maximum entropy problems across different function cases.

Findings

Programs successfully compute Lagrange multipliers for various function types.

Examples demonstrate the practical utility of the Matlab programs.

The methods facilitate maximum entropy distribution calculations in diverse scenarios.

Abstract

The classical Maximum Entropy (ME) problem consists of determining a probability distribution function (pdf) from a finite set of expectations of known functions. The solution depends on $N+1$ Lagrange multipliers which are determined by solving the set of nonlinear equations formed by the $N$ data constraints and the normalization constraint. In this short communication we give three Matlab programs to calculate these Lagrange multipliers. The first considers the general case where the functions can be any functions. The second considers the special case of power functions $x^n$. In this case the data are the geometrical moments of $p(x)$. The third considers the special case of Fourier series functions $\exp(-j n \omega x)$. In this case the data are the trigonometrical moments of $p(x)$. Some examples are also given to illustrate the usefullness of these programs.