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Statistical distance. In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
Hellinger distance. In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f -divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by ...
Bhattacharyya distance. In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributions. [1] It is closely related to the Bhattacharyya coefficient, which is a measure of the amount of overlap between two statistical samples or populations.
Kullback–Leibler divergence. In mathematical statistics, the Kullback–Leibler ( KL) divergence (also called relative entropy and I-divergence [1] ), denoted , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. [2] [3] Mathematically, it is ...
Earth mover's distance. In computer science, the earth mover's distance ( EMD) [1] is a measure of dissimilarity between two frequency distributions, densities, or measures, over a metric space D . Informally, if the distributions are interpreted as two different ways of piling up earth (dirt) over D, the EMD captures the minimum cost of ...
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a distance measure for probability distributions. It is an example of a statistical distance metric, and is sometimes called the statistical distance, statistical difference or variational ...
The Anderson–Darling and Cramér–von Mises statistics belong to the class of quadratic EDF statistics (tests based on the empirical distribution function). If the hypothesized distribution is , and empirical (sample) cumulative distribution function is , then the quadratic EDF statistics measure the distance between and by
Jensen–Shannon divergence. In probability theory and statistics, the Jensen – Shannon divergence is a method of measuring the similarity between two probability distributions. It is also known as information radius ( IRad) [1] [2] or total divergence to the average. [3] It is based on the Kullback–Leibler divergence, with some notable ...