DataVisualizations (version 1.1.12)

ParetoDensityEstimation: Pareto Density EstimationV2

Description

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

Usage

ParetoDensityEstimation(Data, paretoRadius, kernels = NULL,
  MinAnzKernels = 100,PlotIt=FALSE)

Arguments

Data

numeric vector of data.

paretoRadius

Optional, numeric value, see ParetoRadius, Please do not set manually

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

PlotIt

Optional, if TRUE: raw basic r plot of density estimation of debugging purposes. Usually please use ggplot2 interface via PDEplot or MDplot

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 of defining the radius

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. This is the best density estimation to judge Gaussian Mixtures of the data see [Ultsch 2003]

References

Ultsch, A.: Pareto density estimation: A density estimation for knowledge discovery, 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

PDEplot

MDplot

Examples

# NOT RUN {
   data = c(rnorm(1000),rnorm(2000)+2,rnorm(1000)*2-1)
   pdeVal        <- ParetoDensityEstimation(data)
   plot(pdeVal$kernels,pdeVal$paretoDensity,type='l',xaxs='i',
   yaxs='i',xlab='Data',ylab='PDE')
   


# }