The Nearest Neighbor Spacing Distribution (NNSD) is one of the commonly used methods in statistical analysis of regular and chaotic behaviors of nuclear spectra. In this paper, Maximum Likelihood Estimation (MLE) method is proposed to evaluate the parameter of (NNSD)s. We estimate the parameter of (NNSD)s for different mass groups, nuclei with special values of deformation parameter () and also for nuclear spectra correspond to three dynamical symmetry limits and transition regions in the framework of the Interacting Boson Model (IBM) (with pure experimental data). The obtained results confirm theoretical predictions even in cases where the small size of data does not allow definite conclusions with the other methods. Also the ML estimated parameters have minimum uncertainty with variations very close (much closer than those obtained by other methods) to the so called Cramer-Rao Lower Bound (CRLB). ML estimated values predict more regular dynamics in compare to what other estimation methods indicate. We have also evaluated CRLB for all distributions (Brody, Berry-Robnik and Abul-Magd) with both values obtained from MLE and in different sequences where Brody distribution has the least CRLB.

In this paper, we have considered the interplay between phase transitions and configuration mixing of intruder excitations in the [118][119][120][121][122][123][124][125][126][127][128]

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