What does MONOTONE LIKELIHOOD RATIO stand for? 

Monotone likelihood ratio

In statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions (PDFs). Formally, distributions ƒ(x) and g(x) bear the property if for every x 1 > x 0 , f ( x 1 ) g ( x 1 ) ≥ f ( x 0 ) g ( x 0 ) {\displaystyle {\text{for every }}x_{1}>x_{0},\quad {\frac {f(x_{1})}{g(x_{1})}}\geq {\frac {f(x_{0})}{g(x_{0})}}} that is, if the ratio is nondecreasing in the argument x {\displaystyle x} . If the functions are first-differentiable, the property may sometimes be stated ∂ ∂ x ( f ( x ) g ( x ) ) ≥ 0 {\displaystyle {\frac {\partial }{\partial x}}\left({\frac {f(x)}{g(x)}}\right)\geq 0} For two distributions that satisfy the definition with respect to some argument x, we say they "have the MLRP in x." For a family of distributions that all satisfy the definition with respect to some statistic T(X), we say they "have the MLR in T(X)."

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