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In statistics, probability theory and information theory, a statistical distance either measures the distance of an observation from a population or measures the distance between populations. In the later case, the distances can be interpreted as measuring the distances between two probability distributions and hence are essentially measures of distances between probability measures. In some contexts, statistical distance measures relate to the differences between random variables which may have statistical dependence,[1] and hence these are not directly related to measures of distances between probability measures. Statistical distance measures are mostly not metrics and they need not be symmetric. Some types of distance measures are referred to as (statistical) divergences. Information theoretic approaches f-divergence: includes Kullback–Leibler divergence Hellinger distance Total variation distance Renyi's divergence Jensen–Shannon divergence Probability measure based approaches Lévy–Prokhorov metric Bhattacharyya distance Wasserstein metric: also known as the Kantorovich metric, or earth mover's distance Other approaches Signal-to-noise ratio distance Mahalanobis distance Distance correlation is a measure of dependence between two random variables, it is zero if and only if the random variables are independent. The continuous ranked probability score is a measure how good forecasts that are expressed as probability distributions are in matching observed outcomes. Both the location and spread of the forecast distribution are taken into account in judging how close the distribution is the observed value: see probabilistic forecasting. See also Probabilistic metric space Notes ^ Dodge, Y. (2003)—entry for distance References Dodge, Y. (2003) Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9 This statistics-related article is a stub. You can help Wikipedia by expanding it. v • d • e This probability-related article is a stub. You can help Wikipedia by expanding it. v • d • e