Theoretic distributions

• Normal distribution
• Log normal distribution
• Uniform distribution
• Exponential distribution
• Chi-squared distribution

Kolmogorov-Smirnov Tests

• for Normal distribution
• for Log normal distribution
• for Uniform distribution
• for Exponential distribution
• for Chi-squared distribution
• for the same distribution of two samples

Multivariate Linear Regression

Correlation

• Pearson correlation (classic)
• Kendall correlation (robust)
• Spearman correlation (robust)
• Calculation of correlation matrix
• Hierarchical clustering on correlation matrix (creates groups of dimensions)

Covariance matrix

• Classic covariance matrix
• MCD covariance matrix (robust)

Applications using the covariance matrix

• Mahalanobis distance / Robust distance
• Principal Component Analysis (classic / robust)
• Multivariate outlier detection

Clustering

• k means clustering
• Fuzzy k means clustering

Transformations

• Absolute transformation
• Square root transformation
• Logarithmic transformation (ln, log10)
• Z standardization (classic, robust, a-robust)
• Linear Scale to [0,1] interval
• Linear Scale (zero preserving)

Moments

• Arithmetic mean, a-trimmed mean, median
• Standard deviation, variance, MAD, a-trimmed standard deviation, mean of absolute deviations
• Skewness, kurtosis
• Quantiles, quartiles, Inter Quartile Range (IQR)
• 1D outlier detection

Utilities

• Ranks
• Number of unique values
• Unique values
• k smallest element (expected running time O(n))
• Manhatten / Euclidean distances (with dimension weighting)
• Matrix inversion
• Determinant of a matrix