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:
“... a worker was seldom so much annoyed by what he got as by what he got in relation to his fellow workers.”
—Mary Barnett Gilson (1877–?)
“Parents ought, through their own behavior and the values by which they live, to provide direction for their children. But they need to rid themselves of the idea that there are surefire methods which, when well applied, will produce certain predictable results. Whatever we do with and for our children ought to flow from our understanding of and our feelings for the particular situation and the relation we wish to exist between us and our child.”
—Bruno Bettelheim (20th century)
“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)