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:
“Even the simple act that we call “going to visit a person of our acquaintance” is in part an intellectual act. We fill the physical appearance of the person we see with all the notions we have about him, and in the totality of our impressions about him, these notions play the most important role.”
—Marcel Proust (1871–1922)
“Welcome to the great American two-career family and pass the aspirin please.”
—Anastasia Toufexis (20th century)