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The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909. [ 1 ] [ 2 ] It is sometimes called the Jeffreys distance.
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.
Total variation distance (sometimes just called "the" statistical distance) Hellinger distance; Lévy–Prokhorov metric; Wasserstein metric: also known as the Kantorovich metric, or earth mover's distance; Mahalanobis distance; Amari distance; Integral probability metrics generalize several metrics or pseudometrics on distributions
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
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.
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 ...
Other notable measures of distance include the Hellinger distance, histogram intersection, Chi-squared statistic, quadratic form distance, match distance, Kolmogorov–Smirnov distance, and earth mover's distance.