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

Best Probability Density Function for Random Sampled Data

Received: 9 October 2009; Accepted: 2 December 2009 / Published: 4 December 2009
(This article belongs to the Special Issue Maximum Entropy)
Download PDF [1356 KB, uploaded 4 December 2009]
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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Jacobs DJ. Best Probability Density Function for Random Sampled Data. Entropy. 2009; 11(4):1001-1024.

Chicago/Turabian Style

Jacobs, Donald J. 2009. "Best Probability Density Function for Random Sampled Data." Entropy 11, no. 4: 1001-1024.


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