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In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as
The Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the ...
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.
The distribution has important applications in various fields, including econometrics, Bayesian statistics, life testing. [3] In econometrics, the ( α , θ ) parameterization is common for modeling waiting times, such as the time until death, where it often takes the form of an Erlang distribution for integer α values.
A Stein discrepancy is a statistical divergence between two probability measures that is rooted in Stein's method.It was first formulated as a tool to assess the quality of Markov chain Monte Carlo samplers, [1] but has since been used in diverse settings in statistics, machine learning and computer science.
The only divergence on that is both a Bregman divergence and an f-divergence is the Kullback–Leibler divergence. [ 6 ] If n ≥ 3 {\displaystyle n\geq 3} , then any Bregman divergence on Γ n {\displaystyle \Gamma _{n}} that satisfies the data processing inequality must be the Kullback–Leibler divergence.