Monotone likelihood ratio property
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Monotone likelihood ratio property is a set of probability density functions, or PDFs, assumed in theoretical models to characterize risks and uncertanty, which makes more conclusions feasible and often plausible.
[edit] Hypothesis Testing
The monotone likelihood ratio property can be used in hypothesis tests, primarily when dealing with composite null hypotheses.
A joint distribution fθ(x) is said to have the monotone likelihood ratio (MLR) in the statistic T(X) if for any two values θ1 < θ2, the ratio 
depends on X only through T(X), and this ratio is non-decreasing in T(X). If such a joint distribution has this property, a uniformly most powerful test can easily be determined for the hypotheses H0:θ ≤ θ0 versus H1:θ > θ0.
[edit] Example
Example: Let e ("effort") be an input variable into a stochastic production function, and y be the random variable that represent output. Let f(y | e) be the pdf of y for each e. Then the statement that f() has the monotone likelihood ratio property (MLRP) is the same as the statement that: for e2>e1, f(y|e2)/f(y|e1) is increasing in y.
Let y be the random variable that represents the output. E (effort) will be the input variable into a stochastic production function. If F(Y|E) is the pdf of Y for each E, then the statement that F() has the monotone likelihood ratio property (MLRP) is the same as the statement that:
E2>E1, F( Y | E2 ) / F( Y | E1 ) is increasing in Y
[edit] References
- Moffatt, Mike (2006). Monotone Likelihood Ratio Property. About, Inc.. Retrieved on 2006-10-26.
