Relative concentration theory studies the degree of inequality between two
vectors (a(1),....,a(N)) and (alpha (1),....,alpha (N)). It extends concent
ration theory in the sense that, in the latter theory, one of the above vec
tors is (1/N,....,1/N) (N coordinates).
When studying relative concentration one can consider the vectors (a(1),...
.,a(N)) and (alpha (1),.....,alpha (N)) as interchangeable (equivalent) or
not. In the former case this means that the relative concentration of (a(1)
,....,a(N)) versus (alpha (1),....,alpha (N)) is the same as the relative c
oncentration of (alpha (1),.....,alpha (N)) versus (a(1),....,a(N)). We dea
l here with a symmetric theory of relative concentration. In the other case
one wants to consider (a(1),....,a(N)) as having a different role as and h
ence the results can be different when interchanging the vectors. This lead
s to an asymmetric theory of relative concentration.
In this paper we elaborate both models, As they extend concentration theory
, both models use the Lorenz order and Lorenz curves.
For each theory we present good measures of relative concentration and give
applications of each model.