  In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation
method is used to investigate statistical properties of nuclear spectra. The
deviation to regular or chaotic dynamics, is exhibited by closer distances to
Poisson or Wigner limits respectively which evaluated by Kullback-Leibler
Divergence (KLD) measure. Spectral statistics of different sequences prepared
by nuclei corresponds to three dynamical symmetry limits of Interaction Boson
Model(IBM), oblate and prolate nuclei and also the pairing effect on nuclear
level statistics are analyzed (with pure experimental data). KD-based estimated
density function, confirm previous predictions with minimum uncertainty
(evaluated with Integrate Absolute Error (IAE)) in compare to Maximum
Likelihood (ML)-based method. Also, the increasing of regularity degrees of
spectra due to pairing effect is reveal.
