Best probability density function for random sampled data

The maximum entropy method is a theoretically sound approach to construct an analytical form for the probability density function (pdf) given a sample of random events. In practice, numerical methods employed to determine the appropriate Lagrange multipliers associated with a set of moments are generally unstable in the presence of noise due to limited sampling. A robust method is presented that always returns the best pdf, where tradeoff in smoothing a highly varying function due to noise can be controlled. An unconventional adaptive simulated annealing technique, called funnel diffusion, determines expansion coefficients for Chebyshev polynomials in the exponential function.