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

Investigation of level spacing distribution of nuclear energy levels by maximum likelihood estimation method