Monotone Likelihood Ratio - Relation To Other Statistical Properties

Relation To Other Statistical Properties

If a family of distributions has the monotone likelihood ratio property in ,

  1. the family has monotone decreasing hazard rates in (but not necessarily in )
  2. the family exhibits the first-order (and hence second-order) stochastic dominance in, and the best Bayesian update of is increasing in .

But not conversely: neither monotone hazard rates nor stochastic dominance imply the MLRP.

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