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Statistics Definition

  1. May 10, 2010 #1
    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.
  2. jcsd
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