Best Probability Density Function for Random Sampled Data.

Entropy
Donald J Jacobs

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.

References

Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K BandyopadhyayD A Drabold

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Citations

Apr 8, 2017·Accident; Analysis and Prevention·Dennis BöhmländerThomas Brandmeier
May 12, 2018·PloS One·Jenny Farmer, Donald Jacobs

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