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
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