The log-likelihood function is defined to be the natural
logarithm of the likelihood function .
More precisely, ,
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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References Rodriguez, G. "Lecture Notes on Generalized Linear Models." 2007. http://data.princeton.edu/wws509/notes/ . Sun,
D. and Xiao, F. "Likelihood Theory with Score Function." 2013. http://www.stats.uwo.ca/faculty/bellhouse/Likelihood_Theory_with_Score_Function.pdf
Cite this as:
Stover, Christopher . "Log-Likelihood Function." From MathWorld --A Wolfram Web Resource, created by Eric
W. Weisstein . https://mathworld.wolfram.com/Log-LikelihoodFunction.html

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