Likelihood

Definition

Definition

It is assumed that the realisations $x_1, \dots , x_n$ of the random variables $X_1, \dots, X_n$ are observed. The function

$$\theta \rightarrow \prod_{i=1}^n f_\theta(x_i)$$

is called the likelihood of $\theta$ for the realisations $(x_1, \dots, x_n)$ and is noted $L(\theta; x_1, \dots, x_n)$ or simply $L(\theta)$ if there is no ambiguity.

Results

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