Likelihood Function

Topics: Statistics - Random Sample

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(definition)

Let $X_1,\dots ,X_n$ be a random sample with a density function $f(x\mid \theta )$ (i.e. $f(x)$ with a parameter $\theta$).

The sample’s likelihood function (función de verosimilitud in Spanish) $\mathrm{L}(\theta \mid x)$ is defined as:

$$\mathrm{L}(\theta \mid x)=\prod _{i=1}^{n}f(x_i\mid \theta )$$