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1.6×10 −1: Gaussian distribution: probability of a value being more than 1 standard deviation from the mean on a specific side [20] 1.7×10 −1: Chance of rolling a '6' on a six-sided die: 4.2×10 −1: Probability of being dealt only one pair in poker 5.0×10 −1: Chance of getting a 'head' in a coin toss.
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 probability theory, integral probability metrics are types of distance functions between probability distributions, defined by how well a class of functions can distinguish the two distributions. Many important statistical distances are integral probability metrics, including the Wasserstein-1 distance and the total variation distance .
The information geometry definition of divergence (the subject of this article) was initially referred to by alternative terms, including "quasi-distance" Amari (1982, p. 369) and "contrast function" Eguchi (1985), though "divergence" was used in Amari (1985) for the α-divergence, and has become standard for the general class. [1] [2]
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, [1] nearest-neighbor distribution function [2] or nearest neighbor distribution [3] is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned ...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).
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 .
Energy distance satisfies all axioms of a metric thus energy distance characterizes the equality of distributions: D(F,G) = 0 if and only if F = G. Energy distance for statistical applications was introduced in 1985 by Gábor J. Székely, who proved that for real-valued random variables (,) is exactly twice Harald Cramér's distance: [1]