Monotone Likelihood Ratio

Definition

$L(\theta |\mathbf{x})$ has a monotone likelihood ratio (MLR) property in $y=u(\mathbf{x})$ If $\forall {\theta }_1<{\theta }_2,\frac{L({\theta }_1|\mathbf{x})}{L({\theta }_2|\mathbf{x})}$ is a monotone function of $y=u(\mathbf{x})$