  A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the
Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new
ensemble is then applied to the analysis of the chaotic properties of the low
lying collective states of nuclei described by the Interacting Boson Model
(IBM). This model undergoes a transition order-chaos-order from the $SU(3)$
limit to the $O(6)$ limit. Our analysis shows that the quantum fluctuations of
the IBM Hamiltonian, both of the spectrum and the eigenvectors, follow the
expected behaviour predicted by the DGOE when one goes from one limit to the
other.
