KStestMixtures {AdaptGauss} | R Documentation |

## 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.

*AdaptGauss*version 1.6 Index]