Relation To Other Statistical Properties
If a family of distributions has the monotone likelihood ratio property in ,
- the family has monotone decreasing hazard rates in (but not necessarily in )
- 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.
Read more about this topic: Monotone Likelihood Ratio
Famous quotes containing the words relation to, relation and/or properties:
“The adolescent does not develop her identity and individuality by moving outside her family. She is not triggered by some magic unconscious dynamic whereby she rejects her family in favour of her peers or of a larger society.... She continues to develop in relation to her parents. Her mother continues to have more influence over her than either her father or her friends.”
—Terri Apter (20th century)
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)