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Skewness
Statistical measure quantifying the asymmetry of a distribution around its mean, where skewness > 0 indicates right skewness and skewness < 0 indicates left skewness.
Variance stabilization
Process of transforming data to make the variance homogeneous across different levels of the variable, an essential condition for the application of many statistical and ML models.
Power transformation
Family of transformations of the form x^λ where λ is an optimized parameter, including root transformations (λ=0.5), square transformations (λ=2) and log as a limiting case (λ→0).
Gaussian distribution
Normal distribution characterized by its symmetric bell curve, a frequent objective of transformations to satisfy the assumptions of many statistical algorithms.
Lambda parameter
Optimization parameter in Box-Cox and Yeo-Johnson transformations determined by maximum likelihood, controlling the intensity and shape of the applied transformation.
Inverse hyperbolic transformation
Application of the asinh(x) or artanh(x) function to handle distributions with extremes or bounds, offering a robust alternative to logarithmic transformations.
Q-Q Plot
Quantile-quantile plot comparing the empirical distribution of data to a theoretical distribution (often normal), an essential visual tool for evaluating the effectiveness of transformations.
Normality test
Statistical tests (Shapiro-Wilk, Anderson-Darling, Kolmogorov-Smirnov) formally assessing whether data follow a normal distribution after transformation.
Johnson Transformation
System of flexible transformations based on three families (SB, SU, SL) that can approximate any continuous distribution, offering more flexibility than Box-Cox for complex distributions.
Kurtosis
Measure of the flatness or peakedness of a distribution compared to the normal distribution, influencing the choice of appropriate transformation to normalize data.
Quantile Transformation
Non-parametric method transforming data into a specific distribution (normal, uniform) by mapping empirical quantiles to target quantiles.
Log-normal Distribution
Distribution whose logarithm follows a normal law, common in multiplicative phenomena and an ideal candidate for logarithmic transformation.
Arcsine Transformation
Application of arcsin(√x) to proportions and percentages bounded between 0 and 1, stabilizing variance for binomial or frequency data.
Maximum Likelihood
Optimization method used to determine the optimal λ parameter in Box-Cox and Yeo-Johnson transformations by maximizing the likelihood function.