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Entropy 2009, 11(4), 1001-1024; doi:10.3390/e11041001

Best Probability Density Function for Random Sampled Data

Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC, USA
Received: 9 October 2009 / Accepted: 2 December 2009 / Published: 4 December 2009
(This article belongs to the Special Issue Maximum Entropy)
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Abstract

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.
Keywords: maximum entropy method; probability density function; Lagrange multipliers; level-function moments; least squares error; adaptive simulated annealing; smoothing noise maximum entropy method; probability density function; Lagrange multipliers; level-function moments; least squares error; adaptive simulated annealing; smoothing noise
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Jacobs, D.J. Best Probability Density Function for Random Sampled Data. Entropy 2009, 11, 1001-1024.

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