  The nearest neighbor spacing distribution (NNSD) is one of common methods in
statistical analysis of nuclear energy levels. In this paper, we have proposed
Maximum Likelihood Estimation (MLE) method to evaluate parameter of (NNSD)'s
which explain chaotic and regular behavior of nuclear systems .Also with
Cramer-Rao Lower Bound (CRLB) will obtain decreasing of uncertainty for our
results in compare to previous methods. We calculate these parameters for
different mass groups and nuclei with special values of deformation parameter,
and also for nuclei with IBM's three dynamical symmetries and transitional
regions between these three limits and confirm theoretical predictions even in
cases where the small size of data don't allow exact conclusions with previous
methods . We obtain better consistent of our results with Poisson and
Wigner(GOE) distributions with Kullback-Leibeller divergence.
