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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.
The total variation distance is half of the L 1 distance between the probability functions: on discrete domains, this is the distance between the probability mass functions [4] (,) = | () |, and when the distributions have standard probability density functions p and q, [5]
The definition of the Hausdorff distance can be derived by a series of natural extensions of the distance function (,) in the underlying metric space M, as follows: [7] Define a distance function between any point x of M and any non-empty set Y of M by: (,) = {(,)}.
In mathematics, the Wasserstein distance or Kantorovich–Rubinstein metric is a distance function defined between probability distributions on a given metric space. It is named after Leonid Vaseršteĭn .
In statistics, Cohen's h, popularized by Jacob Cohen, is a measure of distance between two proportions or probabilities. Cohen's h has several related uses: It can be used to describe the difference between two proportions as "small", "medium", or "large". It can be used to determine if the difference between two proportions is "meaningful".
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.
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In statistics, Gower's distance between two mixed-type objects is a similarity measure that can handle different types of data within the same dataset and is particularly useful in cluster analysis or other multivariate statistical techniques. Data can be binary, ordinal, or continuous variables.