Given a function defined over a parabolic subgroup of a Coxeter group,
equidistributed with the length, we give a procedure to construct a function
over the entire group, equidistributed with the length. Such a procedure
permits to define functions equidistributed with the length in all the finite
Coxeter groups. We can establish our results in the general setting of graded
posets which satisfy some properties. These results apply to some known
functions arising in Coxeter groups as the major index, the negative major
index and the D-negative major index defined in type A, B and D
respectively
