A non-parametric estimation approach in the investigation of spectral statistics

Abstract

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.

Pairing effect on spectral statistics of even and odd mass nuclei

“…Even-Even nuclei 34 S, 38 Ar, 42 The GOE KLD measures which determine the distance of KD-based estimated functions to GOE (chaotic) limit, propose similar statistics that suggested by ML-based estimated values for considered systems. Also the obvious reductions in the uncertainties of KDE-based estimated function (the uncertainties have evaluated with Mean Absolute Error method [27][28]) have occurred, therefore, we can conclude, the KDE-based function yield the closer density function to real and exact distribution of every sequences. These results, namely, more regular dynamics for even-mass nuclei in compare to odd-mass ones may be interpreted that the pairing force between the single particle and collective degrees of freedom is weaker in odd-mass nuclei than even-mass nuclei.…”

“…2 + and 4 + levels of even-and also1 2 ,3 2 , 5 2 + + + levels of odd-mass nuclei in which the spin-parity J π assignment of at least five consecutive levels are definite, levels are combined in several ways to search for effects due to mass, the intensity of pairing and also the types of pairs on the spectral statistics. Also, we have used the Maximum Likelihood (ML) [26] and Kernel Density (KD) estimation [27][28] techniques to consider the spectral statistics of sequences with high accuracy by both parametric and non-parametric estimation methods, respectively. This paper is organized as follows: Section 2 briefly summarizes the theoretical aspects of pairing Hamiltonian and data sets which have used in this analysis.…”

“…calculate the distance ofˆ( ) f x related to GOE (or Poisson) limit via Kullback-Leibler Divergence (KLD) measure which define as[27] our estimated distribution function by MLE or KLD techniques, Poisson or GOE distributions are regard as ( ) i Q X . The KLD measure is a non-symmetric measure to exhibit the average of the logarithmic difference between the probability distributions ( ) between two probability distribution functions, therefore, a closer distances to Poisson or GOE limits, explore regular or chaotic dynamics of sequences, respectively.…”

Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques

“…In comparison with parametric estimation, non-parametric estimation method does not need to assume the error distribution in advance, thus its estimation result is closer to the actual value. Commonly used non-parametric estimation methods include histogram density estimation and kernel density estimation, in which the latter is more simple and efficient in practical application [33,[43][44][45]. Therefore, the kernel density estimation method is applied for density function estimation and confidence interval calculation.…”

Using kernel density estimation to model surgical procedure duration

“…Kernel density estimation borrows its intuitive approach from the familiar histogram, which is among the most common nonparametric density estimation techniques (Jafarizadeh, Fouladi, Sabri, & Maleki, 2011;Scott, 2009). The univariate histogram is constructed by specification of a series of adjacent bins, or sub-intervals, that cover the domain of the variable.…”