Jeffreys distance

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