AdaptGauss (version 1.2.0)

Chi2testMixtures: Pearson's chi-squared test

Description

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

Usage

Chi2testMixtures(Data,Means,SDs,Weights,IsLogDistribution,PlotIt,UpperLimit,VarName)

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

VarName

If PlotIt=TRUE, the name of the inspected variable, default 'Data'

Value

• List with
• Pvalue
  Pvalue of a suiting chi-square , Pvalue ==0 if Pvalue <0.001< description="">
• BinCenters
  bin centers
• ObsNrInBin
  No. of data in bin
• ExpectedNrInBin
  No. of data that should be in bin according to GMM
• Chi2Value
  the TestStatistic i.e.: sum((ObsNrInBin(Ind)-ExpectedNrInBin(Ind))^2/ExpectedNrInBin(Ind)) with Ind = find(ExpectedNrInBin>=10)

Details

Let O_i be the observed features and E_i be the expected number E, than the test statistic is defined with T=sum((O_i-E_i)^2/E_i)*1/m, where m the number of data points. The expected number Ei may be derived for each bin with the null hypothesis that the data is from the distribution. Further details, see [Thrun & Ultsch, 2015].

References

Hartung, J., Elpelt, B., and Kloesener, K.H.: Statistik, 8. Aufl. Verlag Oldenburg (1991). Thrun, M. C., Ultsch, A.: Models of Income Distributions for Knowledge Discovery, European Conference on Data Analysis, DOI 10.13140/RG.2.1.4463.0244, pp. 28-29, Colchester 2015.