We model a set of observations as a random sample from an unknown joint probability distribution which is expressed in terms of a set of parameters. The goal of maximum … See more

It may be the case that variables are correlated, that is, not independent. Two random variables $${\displaystyle y_{1}}$$ and $${\displaystyle y_{2}}$$ are independent only if … See more

Except for special cases, the likelihood equations
$${\displaystyle {\frac {\partial \ell (\theta ;\mathbf {y} )}{\partial \theta }}=0}$$
cannot be solved explicitly for an estimator
where the vector See more

A maximum likelihood estimator is an extremum estimator obtained by maximizing, as a function of θ, the objective function See more

Discrete uniform distribution
Consider a case where n tickets numbered from 1 to n are placed in a box and one is selected at random (see uniform distribution); thus, the sample size is 1. If n is unknown, then the maximum likelihood estimator See more

Early users of maximum likelihood include Carl Friedrich Gauss, Pierre-Simon Laplace, Thorvald N. Thiele, and Francis Ysidro Edgeworth. It was Ronald Fisher however, between … See more

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Related concepts
• Akaike information criterion: a criterion to compare statistical models, based on MLE
• Extremum estimator: a more general class of estimators to which MLE belongs See more