Likelihood equation

An equation obtained by the maximum-likelihood method when finding statistical estimators of unknown parameters. Let be a random vector the probability density of which contains an unknown parameter . Then the equation

is called the likelihood equation and its solution is called the maximum-likelihood estimator for . In some cases the likelihood equation can be solved in an elementary way. However, in general, the likelihood equation is an algebraic or transcendental equation, solved by the method of successive approximation (cf. Sequential approximation, method of).

References

[1]	B.L. van der Waerden, "Mathematische Statistik" , Springer (1957)

References

[a1]	D.R. Cox, D.V. Hinkley, "Theoretical statistics" , Chapman & Hall (1974) pp. 21