  Lorenz values and the Gini index are popular quantities in Mathematical
Economics, and are used here in the context of quantum systems with
finite-dimensional Hilbert space. They quantify the uncertainty in the
probability distribution related to an orthonormal basis. It is shown that
Lorenz values are superadditive functions and the Gini indices are subadditive
functions. The supremum over all density matrices of the sum of the two Gini
indices with respect to position and momentum states, is used to define an
uncertainty coefficient which quantifies the uncertainty in the quantum system.
It is shown that the uncertainty coefficient is positive, and an upper bound
for it is given. Various examples demonstrate these ideas.
