Likelihood function

A function that tells us the likelihood of receiving a certain value based on a particular distribution.

Examples are:

Poisson likelihood function:

Poisson Distributions
The likelihood of getting $k$ successes in many trials with density $λ$ is given by:

p (k) = \frac{λ^{k}}{k!} e^{- λ}

Or, in more statistical terms and including the sampling effort (offset) $E_{i}$

p (y_{i} | E_{i} λ_{i}) = \frac{(E_{i} λ_{i})^{y_{i}} e^{E_{i} λ_{i}}}{y_{i}!}