Likelihood function
Relative likelihood function

Since the actual value of the likelihood function depends on the sample, it is often convenient to work with a standardized measure. Suppose that the maximum likelihood estimate for the parameter θ is θ ^ {\textstyle {\hat {\theta }}}. Relative plausibilities of other θ values may be found by comparing the likelihoods of those other values with the likelihood of θ ^ {\textstyle {\hat {\theta }}}. The relative likelihood of θ is defined to be R (θ) = L (θ ∣ x) L (θ ^ ∣ x). {\displaystyle R(\theta)={\frac {{\mathcal {L}}(\theta \mid x)}{{\mathcal {L}}({\hat {\theta }}\mid x)}}.} Thus, the relative likelihood is the likelihood ratio (discussed above) with the fixed denominator L (θ ^) {\textstyle {\mathcal {L}}({\hat {\theta }})}. This corresponds to standardizing the likelihood to have a maximum of 1.
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