Important Case: The Exponential Family
Although the Karlin-Rubin theorem may seem weak because of its restriction to scalar parameter and scalar measurement, it turns out that there exist a host of problems for which the theorem holds. In particular, the one-dimensional exponential family of probability density functions or probability mass functions with
has a monotone non-decreasing likelihood ratio in the sufficient statistic T(x), provided that is non-decreasing.
Read more about this topic: Uniformly Most Powerful Test
Famous quotes containing the words important and/or family:
“The knocking out of a pipe can be made almost as important as the smoking of it, especially if there are nervous people in the room. A good, smart knock of a pipe against a tin wastebasket and you will have a neurasthenic out of his chair and into the window sash in no time.”
—Robert Benchley (1889–1945)
“What we often take to be family values—the work ethic, honesty, clean living, marital fidelity, and individual responsibility—are in fact social, religious, or cultural values. To be sure, these values are transmitted by parents to their children and are familial in that sense. They do not, however, originate within the family. It is the value of close relationships with other family members, and the importance of these bonds relative to other needs.”
—David Elkind (20th century)