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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.
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.
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 statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
The two most important divergences are the relative entropy (Kullback–Leibler divergence, KL divergence), which is central to information theory and statistics, and the squared Euclidean distance (SED). Minimizing these two divergences is the main way that linear inverse problems are solved, via the principle of maximum entropy and least ...
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 much a model probability distribution Q is different from a true probability distribution P.
The Euclidean distance formula is used to find the distance between two points on a plane, which is visualized in the image below. Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses. [citation needed] When you generalize the Euclidean distance formula and Manhattan ...
The Mahalanobis distance is a measure of the distance between a point and a distribution, introduced by P. C. Mahalanobis in 1936. [1] The mathematical details of Mahalanobis distance first appeared in the Journal of The Asiatic Society of Bengal in 1936. [ 2 ]
In statistics, Bhattacharyya angle, also called statistical angle, is a measure of distance between two probability measures defined on a finite probability space. It is defined as It is defined as Δ ( p , q ) = arccos BC ( p , q ) {\displaystyle \Delta (p,q)=\arccos \operatorname {BC} (p,q)}