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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.
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 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 has appeared in the Journal of The Asiatic Society of Bengal. [ 2 ] Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls ...
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 reference probability distribution P is different from a second probability distribution Q. [2][3] Mathematically, it is defined as.
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. Intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on , the metric is the minimum "cost" of turning one ...
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.
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac ...