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Quasi-continuous maximum entropy distribution approximation with kernel density

Author

Listed:
  • Thomas Mazzoni
  • Elmar Reucher

Abstract

This paper extends maximum entropy estimation of discrete probability distributions to the continuous case. This transition leads to a non-parametric estimation of a probability density function, preserving the maximum entropy principle. Furthermore, the derived density estimate provides a minimum mean integrated square error. In the second step, it is shown how boundary conditions can be included, resulting in a probability density function obeying maximum entropy. The criterion for deviation from a reference distribution is the Kullback-Leibler entropy. It is further shown, how the characteristics of a particular distribution can be preserved by using integration kernels with mimetic properties.

Suggested Citation

  • Thomas Mazzoni & Elmar Reucher, 2011. "Quasi-continuous maximum entropy distribution approximation with kernel density," International Journal of Information and Decision Sciences, Inderscience Enterprises Ltd, vol. 3(4), pages 335-350.
    • Handle: RePEc:ids:ijidsc:v:3:y:2011:i:4:p:335-350
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