Rényi Entropy

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α, and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet-triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α.

Two different distributions may have equal Rényi entropy; thus a distribution cannot be identified by its Rényi entropy. In this paper, we explore properties of the Rényi entropy of order statistics. Several characterizations are established based on the Rényi entropy of ...

The mathematical formulation used in tomography has been successfully applied to time-frequency analysis, which represents an important “imaging modality ” of the structure of signals. Based on the interrelation between CT and time-frequency analysis, new methods have been developed for the latter. In this paper, an original method for constructing the time-frequency representation of signals from the squared magnitudes of their fractional Fourier transforms is presented. The method uses α-norm minimization with α → 1 which is motivated by Rényi entropy maximization. An iterative optimization method with adaptive estimation of the convergence parameter is elaborated. The proposed method exhibits advantages in the suppression of interference terms for signals with simple time-frequency configurations.

This paper introduces a new four parameter Rayleigh distribution which generalizes the transmuted generalized Rayleigh distribution introduced by Merovci (2014). The new model is referred to as exponentiated transmuted generalized Rayleigh (ETGR) distribution. Various mathematical properties of the new model including ordinary and incomplete moments, quantile function, generating function and Rényi entropy are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. Two real data sets are used to compare the flexibility of the new model versus other models.

Vagueness in the scientific studies presents a challenging dimension. Intuitionistic fuzzy set theory has emerged as a tool for its characterization. There is need to associate measures which can measure vagueness and differences in the underlying characterizing IFSs. In the present paper we introduce an information theoretic divergence measure, called intuitionistic fuzzy Jensen-Rényi divergence. It is a difference measure in the setting of intuitionistic fuzzy set theory, involving parameters that provide flexibility and choice. The strength of the new measure lies in its properties and applications. Paper investigates some properties in details. Then, an approach to multiple-attribute decision making based on intuitionistic fuzzy Jensen-Rényi divergence is proposed. Paper carries a numerical example illustrating the application of the new measure and the role of various parameters therein to multiple-attribute decision making problem formulated in terms of intuitionistic fuzzy sets.