# Likelihood equation

From Encyclopedia of Mathematics

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) |

#### Comments

#### References

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

**How to Cite This Entry:**

Likelihood equation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Likelihood_equation&oldid=19118

This article was adapted from an original article by M.S. Nikulin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article