# Likelihood Function

From Open Risk Manual

## Definition

The **Likelihood Function** is a very general expression that captures the joint probability of observing a particular statistical sample (under IID assumption) given a particular set of parameters of a parametric statistical moodel

Maximizing the likelihood function (for classes of models where this is tractable) is the standard method of estimating a statistical model's parameters

## Formula

where

- N is the sample size
- is the probability of individual observation given