Monotone Likelihood Ratio
The ratio of the density functions above is increasing in the parameter, so / satisfies the monotone likelihood ratio property.
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 any,
that is, if the ratio is nondecreasing in the argument .
If the functions are first-differentiable, the property may sometimes be stated
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)."
Read more about Monotone Likelihood Ratio: Intuition, Families of Distributions Satisfying MLR, Relation To Other Statistical Properties
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