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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 Ernst Hellinger in 1909.
Ernst David Hellinger (September 30, 1883 – March 28, 1950) was a German mathematician and is primarily known for his works on statistics and probability. His works include Hellinger distance and Hellinger integral which were introduced by him in 1909.
Notably, except for total variation distance, all others are special cases of -divergence, or linear sums of -divergences. For each f-divergence D f {\displaystyle D_{f}} , its generating function is not uniquely defined, but only up to c ⋅ ( t − 1 ) {\displaystyle c\cdot (t-1)} , where c {\displaystyle c} is any real constant.
In mathematics, the Hellinger integral is an integral introduced by Hellinger that is a special case of the Kolmogorov integral. It is used to define the Hellinger distance in probability theory. References
Jaro distance is commonly used in record linkage to compare first and last names to other sources. Edit distance; Levenshtein distance; Lee distance; Hamming distance; Jaro distance; Similarity between two probability distributions. Typical measures of similarity for probability distributions are the Bhattacharyya distance and the Hellinger ...
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 (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.
Hellinger is a surname. Notable people with the surname include: Ernst Hellinger (1883–1950), German mathematician Hellinger distance, used to quantify the similarity between two probability distributions; Hellinger integral, used to define the Hellinger distance in probability theory