Editing Point estimation (section)

=== Method of maximum likelihood (MLE) ===
The [[Maximum likelihood estimation|method of maximum likelihood]], due to R.A. Fisher, is the most important general method of estimation. This estimator method attempts to acquire unknown parameters that maximize the likelihood function. It uses a known model (ex. the normal distribution) and uses the values of parameters in the model that maximize a likelihood function to find the most suitable match for the data.<ref>{{Cite book|title=Categorical Data Analysis|publisher=Agresti A.|year=1990|location=John Wiley and Sons, New York|pages=}}</ref>

Let X = (X<sub>1</sub>, X<sub>2</sub>, ... ,X<sub>n</sub>) denote a random sample with joint p.d.f or p.m.f. f(x, θ) (θ may be a vector). The function f(x, θ), considered as a function of θ, is called the likelihood function. In this case, it is denoted by L(θ). The principle of maximum likelihood consists of choosing an estimate within the admissible range of θ, that maximizes the likelihood. This estimator is called the maximum likelihood estimate (MLE) of θ. In order to obtain the MLE of θ, we use the equation

''dlog''L(θ)/''d''θ<sub>i</sub>=0, i = 1, 2, …, k. If θ is a vector, then partial derivatives are considered to get the likelihood equations.<ref name=":1" />