# Jeffreys distance

From Encyclopedia of Mathematics

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A measure of the divergence between two probability distributions, developed by H. Jeffreys. For probability distributions on a finite set of size $n$, given by $P = (p_1,\ldots,p_n)$ and $Q = (q_1,\ldots,q_n)$, the Jeffreys distance is $$ J(P,Q) = \sum_{i=1}^n \left( { \sqrt{p_i} - \sqrt{q_i} }\right)^2 \ . $$

See also: Kullback–Leibler-type distance measures.

#### References

- Jeffreys, Harold "An invariant form for the prior probability in estimation problems"
*Proc. R. Soc. Lond., Ser. A.***186**(1946) 453-461 DOI 10.1098/rspa.1946.0056 Zbl 0063.03050

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Jeffreys distance.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Jeffreys_distance&oldid=38969