Hellinger Distance - Definition - Measure Theory

Measure Theory

To define the Hellinger distance in terms of measure theory, let P and Q denote two probability measures that are absolutely continuous with respect to a third probability measure λ. The square of the Hellinger distance between P and Q is defined as the quantity

Here, dP / and dQ / dλ are the Radon–Nikodym derivatives of P and Q respectively. This definition does not depend on λ, so the Hellinger distance between P and Q does not change if λ is replaced with a different probability measure with respect to which both P and Q are absolutely continuous. For compactness, the above formula is often written as

Read more about this topic:  Hellinger Distance, Definition

Famous quotes containing the words measure and/or theory:

    ...the measure you give will be the measure you get...
    Bible: New Testament, Mark 4:24.

    Jesus.

    There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.
    —A.J. (Alfred Jules)