Sufficient condition for monotone likelihood ratio property

Question

What are sufficient conditions for the monotone likelihood ratio property? I have a set-up where $F(x)$ (cumulative distribution function of r.v. $x$) always exceeds $G(x)$ (a different cum. distrib. function), when these c.d.f.s are taken as functions with an argument of $x$?

Answer 1

The relationship you're describing is stochastic dominance. You need $f(x)/g(x)$ to be monotonic in $x$, where $f,g$ are the density functions corresponding to $F,G$ to get the MLRP.