MAS 2013 Proceeding

A mechanical approach of multivariate density function approximation

Authors:   László Mohácsi, Orsolya Rétallér


In this paper we are modeling multivariate density functions by going back to the roots instead of trying to fit a well-known copula on the data, we choose to generate one. Our model approximates the two dimensional density function using physical analogy. Points on the scatter plot diagram are represented by small balls of unit mass placed on a sheet of elastic sponge, and the deformation of the surface of the sponge caused by the balls represents the density of the points on the scatter plot diagram. The elasticity of the sponge is described by Hooke's law. The distortion of the sponge can be determined by using finite element methods. The distorted surface can be approximated by functions using Fourier transformation. Hence, the model can be extended into higher dimensions.

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