# Statistics Definition

1. May 10, 2010

### Obie

In statistics, the likelihood ratio of two probability distributions f(x), g(x) with the same support (for simplicity) is L(x)=f(x)/g(x).

It is often simpler to work with the log likelihood l(x)=ln(f(x)/g(x))=ln(f(x))-ln(g(x)).

The Kullback-Liebler information number is defined as E{l(x)} using f(x) as the true distribution i.e. the expected value of the log likelihood when the true distribution is in the NUMERATOR of the likelihood.

Is there a name for the analogous concept but without taking logs?

That is, is there a name for the expected value of the likelihood function E{L(x)} assuming that the true distribution is f(x)?

E{L(x)} =Int over support (f(x)^2)/g(x)

A name or a reference to a book or article would be very helpful.