ABSTRACT
The method of maximum likelihood was formally introduced into statistics by Fisher (1922). Let X1, · · · , Xn be a random sample from a distribution with density f(x; θ) governed by some parameter θ. A maximum likelihood estimator θ̂n for θ is that value of θ which maximises the likelihood
Ln(θ) = n∏
f(Xj ; θ) ,
or equivalently, maximises the log-likelihood
n(θ) = n∑
ln f(Xj ; θ) .
