Functional k-sample problem when data are density functions

This paper deals with the k-sample problem for functional data when the observations are density functions. We introduce test procedures based on distances between pairs of density functions (L1 distance and Hellinger distance, among others). A simulation study is carried out to compare the practical behaviour of the proposed tests. Theoretical derivations have been done in order to allow weighted samples in the test procedures. The paper ends with a real data example: for a collection of European regions we estimate the regional relative income densities and then we test the significance of the country effect.