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Related Concept Videos

Normal Distribution01:11

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The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is observed in almost all disciplines. Some of these include psychology, business, economics, the sciences, nursing, and, of course, mathematics. Some instructors may use the normal distribution to help determine students’ grades. Most IQ scores are normally distributed. Often real-estate prices fit a normal distribution. The normal distribution is extremely...
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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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Related Experiment Video

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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Published on: September 26, 2016

Edgeworth-expanded gaussian mixture density modeling.

Marc M Van Hulle1

  • 1K.U. Leuven, Laboratorium voor Neuro-en Psychofysiologie, Belgium. marc@neuro.kuleuven.ac.be

Neural Computation
|July 27, 2005
PubMed
Summary
This summary is machine-generated.

This study proposes using mixtures of moderate-order Edgeworth-expanded Gaussian kernels instead of high-order expansions. A closed-form solution for parameter estimation is presented, extending to multivariate cases.

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Area of Science:

  • Statistical modeling
  • Kernel density estimation

Background:

  • High-order Edgeworth expansions can be complex.
  • Single Gaussian kernels may lack flexibility.

Purpose of the Study:

  • To introduce a novel approach using mixtures of moderate-order Edgeworth-expanded Gaussian kernels.
  • To develop an efficient parameter estimation method.
  • To extend the method to multivariate distributions.

Main Methods:

  • Utilizing mixtures of Edgeworth-expanded Gaussian kernels.
  • Employing weighted moment matching for parameter estimation.
  • Formulating the multivariate extension.

Main Results:

  • A simple closed-form solution for kernel parameter estimation.
  • Successful extension to the multivariate case.
  • An alternative to high-order single kernel expansions.

Conclusions:

  • Mixtures of moderate-order Edgeworth-expanded Gaussian kernels offer a practical alternative.
  • The proposed method simplifies parameter estimation.
  • The approach is adaptable to multivariate density approximation.