Log-Likelihood Function

The log-likelihood function F(theta) is defined to be the natural logarithm of the likelihood function L(theta). More precisely, F(theta)=lnL(theta), and so in particular, defining the likelihood function in expanded notation as


shows that


The log-likelihood function is used throughout various subfields of mathematics, both pure and applied, and has particular importance in fields such as likelihood theory.

See also

Likelihood, Likelihood Function, Logarithm, Natural Logarithm, Probability

This entry contributed by Christopher Stover

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Rodriguez, G. "Lecture Notes on Generalized Linear Models." 2007., D. and Xiao, F. "Likelihood Theory with Score Function." 2013.

Cite this as:

Stover, Christopher. "Log-Likelihood Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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