Definition
A single element of a random vector is neutral if the relative proportions of all the other elements are independent of . The concept was originally developed for the study of turtle scutes.
Formally, consider the vector of random variables
where
- .
The values are interpreted as lengths whose sum is unity. In a variety of contexts, it is often desirable to eliminate a proportion, say, and consider the distribution of the remaining intervals within the remaining length. The first element of, viz is defined as neutral if is statistically independent of the vector
Variable is neutral if is independent of the remaining interval: that is, being independent of
Thus, viewed as the first element of, is neutral.
In general, variable is neutral if is independent of
A vector for which each element is neutral is completely neutral.
If is drawn from a Dirichlet distribution, then is completely neutral.
Read more about this topic: Neutral Vector
Famous quotes containing the word definition:
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)