The Method of Maximum Likelihood

Definition

Likelihood function

The likelihood function denoted by of n random variables if the joint density of the n random variables, say , which is considerd to be a function of . In particular, if is a random sample from the density , then the likelihood function is .

Maximum-Likelihood Estimator

Let be the likelihood function for the ramdom variables . If as a function of the observations is the value which maximize , then is the maximum likelihood estimator of .