KStestMixtures {AdaptGauss}

Kolmogorov-Smirnov test

Description

Returns a P value and visualizes for Kolmogorov-Smirnov test of Data versus a given Gauss Mixture Model

Usage

KStestMixtures(Data,Means,SDs,Weights,IsLogDistribution,

PlotIt,UpperLimit,NoRepetitions,Silent)

Arguments

Data

vector of data points

Means

vector of Means of Gaussians

SDs

vector of standard deviations, estimated Gaussian Kernels

Weights

vector of relative number of points in Gaussians (prior probabilities)

IsLogDistribution

Optional, if IsLogDistribution(i)==1, then mixture is lognormal, default vector of zeros of length 1:L

PlotIt

Optional, Default: FALSE, do a Plot of the compared cdfs and the KS-test distribution (Diff)

UpperLimit

Optional. test only for Data <= UpperLimit, Default = max(Data) i.e all Data.

NoRepetitions

Optional, default =1000, scalar, Number of Repetitions for monte carlo sampling

Silent

Optional, default=TRUE, If FALSE, shows progress of computation by points (On windows systems a progress bar)

Details

The null hypothesis is that the estimated data distribution does not differ significantly from the GMM. If there is a significant difference, then the Pvalue is small and the null hypothesis is rejected.

Value

List with

Pvalue

Pvalue of a suiting Kolmogorov-Smirnov test, Pvalue ==0 if Pvalue <0.001

DataKernels

such that plot(DataKernels,DataCDF) gives the cdf(Data)

DataCDF

such that plot(DataKernels,DataCDF) gives the cdf(Data)

CDFGaussMixture

No. of data that should be in bin according to GMM

Author(s)

Michael Thrun, Alfred Ultsch

References

Smirnov, N., Table for Estimating the Goodness of Fit of Empirical Distributions. 1948, (2), 279-281.