In statistics, and specifically in the study of the Dirichlet distribution, a neutral vector of random variables is one that exhibits a particular type of statistical independence amongst its elements. In particular, when elements of the random vector must add up to certain sum, then an element in the vector is neutral with respect to the others if the distribution of the vector created by expressing the remaining elements as proportions of their total is independent of the element that was omitted.

Definition

is neutral if the relative.

Formally, consider the vector of random variables

where

is defined as neutral is statistically independent of the vector

being independent of

, is neutral.

is independent of

Complete neutrality

A vector for which each element is neutral is completely neutral.

is completely neutral. In 1980, James and Mosimann showed that the Dirichlet distribution is characterised by neutrality.

See also

• Generalized Dirichlet distribution

References