Log-Likelihood Function

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.

REFERENCES:

Rodriguez, G. "Lecture Notes on Generalized Linear Models." 2007. https://data.princeton.edu/wws509/notes/.

Sun, D. and Xiao, F. "Likelihood Theory with Score Function." 2013. https://www.stats.uwo.ca/faculty/bellhouse/Likelihood_Theory_with_Score_Function.pdf