AdaptGauss (version 1.2.0)

ParetoDensityEstimation: Pareto Density Estimation

Description

This function estimates the Pareto Density for the distribution of one variable.

Usage

ParetoDensityEstimation(Data,paretoRadius,kernels,MinAnzKernels)

Arguments

Data

numeric vector of data.

paretoRadius

Optional, numeric value, see ParetoRadius

kernels

Optional, numeric vector. data values where pareto density is measured at. If 0 (by default) kernels will be computed.

MinAnzKernels

Optional, minimal number of kernels, default MinAnzKernels==100

Value

• List with
• kernels
  numeric vector. data values at with Pareto Density is measured.
• paretoDensity
  numeric vector containing the determined density by ParetoRadius.
• paretoRadius
  numeric value.

Details

Pareto Density Estimation (PDE) is a method for the estimation of probability density functions using hyperspheres. The Pareto-radius of the hyperspheres is derived from the optimization of information for minimal set size. It is shown, that Pareto Density is the best estimate for clusters of Gaussian structure. The method is shown to be robust when cluster overlap and when the variances differ across clusters.

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discover, in Baier, D.; Werrnecke, K. D., (Eds), Innovations in classification, data science, and information systems, Proc Gfkl 2003, pp 91-100, Springer, Berlin, 2005.

See Also

ParetoRadius

Examples

data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
			# Optional, if not given ParetoDensityEstimation() 
			# calls ParetoRadius()
			pareto_radius<-ParetoRadius(data) 
			pdeVal        <- ParetoDensityEstimation(data,pareto_radius)
			plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
			yaxs='i',xlab='Data',ylab='PDE')