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 whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to “the serious.” One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)