Kolmogorov-Smirnov methods

The Kolmogorov-Smirnov method is another method, which may, among other applications, be used to test for normality. The principle of the method involves comparing the sample cumulative distribution function with the... 

When the Kolmogorov-Smirnov method is used to test whether a distribution is normal, we first transform the original data, which might have any values for their mean and standard deviation, into the standard normal variable, z (see Section 2.2). This is done by using the equation ... 

Frequency domain performance has been analyzed with goodness-of-fit tests such as the Chi-square, Kolmogorov-Smirnov, and Wilcoxon Rank Sum tests. The studies by Young and Alward (14) and Hartigan et. al. (J 3) demonstrate the use of these tests for pesticide runoff and large-scale river basin modeling efforts, respectively, in conjunction with the paired-data tests. James and Burges ( 1 6 ) discuss the use of the above statistics and some additional tests in both the calibration and verification phases of model validation. They also discuss methods of data analysis for detection of errors this last topic needs additional research in order to consider uncertainties in the data which provide both the model input and the output to which model predictions are compared. 

Normality of the distribution of results is checked by the Kolmogorov-Smirnov test and outlier tests are performed on variances and means. ANOVA is used to calculate the different contributions to the variance, between laboratory, between method, and within laboratory. 

Roughly, about 250 data points are required to fit the generalized hyperbolic distributions. However, about 100 data points can offer reasonable results. Although maximum-likelihood estimation method can be used to estimate the parameters, it is very difficult to solve such a complicated nonlinear equation system with five equations and five unknown parameters. Therefore, numerical algorithms are suggested such as modified Powell method (Wang, 2005). Kolmogorov-Smirnov statistics can also be used here for the fitness test. 

Similar to the CSE method [20], Kolmogorov-Smirnov test (KS) was used to assess the activity of a fragment For this purpose, the activity distribution of compounds belonging to a fragment was compared with the activity distribution... 

Byvatov and Schneider compared the SVM-based and the Kolmogorov-Smirnov feature selection methods to characterize ligand-receptor interactions in focused compound libraries.Three datasets were used to compare the feature selection algorithms 226 kinase inhibitors and 4479 noninhibitors 227 factor Xa inhibitors and 4478 noninhibitors and 227 factor Xa inhibitors and 195 thrombin inhibitors. SVM classifiers with a degree 5 polynomial kernel were used for all computations, and the molecular structure was encoded into 182 MOE descriptors and 225 topological pharmacophores. In one test, both feature selection algorithms produced comparable results, whereas in all other cases, SVM-based feature selection had better predictions. 

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