Skewness and Kurtosis: From Moments to Machine Learning

Statistical moments are the building blocks for describing the shape of a data distribution. Skewness, derived from the third central moment, measures the asymmetry of the distribution, indicating whether the tail is longer on the right (positive skew) or left (negative skew). Kurtosis, related to the fourth central moment, describes the weight of the distribution's tails, not its peak, identifying distributions with heavy tails (leptokurtic) or light tails (platykurtic). Understanding these measures is crucial in machine learning for exploratory data analysis and determining if data transformations, like log or Box-Cox, are needed to handle non-normal distributions.