New Generalized Parametric Measures of Entropy and Cross Entropy
نویسنده
چکیده
The measure of entropy introduced by Shannon [12] is the key concept in the literature of information theory and has found tremendous applications in different disciplines of science and technology. The various researchers have generalized this entropy with different approaches. The object of the present manuscript is to develop a generalized measure of entropy by using the property of concavity. The proposed measure satisfies all essential and some desirable properties of the original Shannon’s [12] entropy. Moreover, we have developed a new generalized measure of cross entropy which corresponds to the newly introduced measure of entropy.
منابع مشابه
Generalized Cross-Entropy Methods
The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper we investigate how these methods can be extended to provide a general non-parametric cross-entropy framework based on φ-divergence distance measures. We show how the χ distance in particular yields a viable alternative to Kull...
متن کاملSome properties of the parametric relative operator entropy
The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...
متن کاملGeneralized Cross-entropy Methods with Applications to Rare-event Simulation and Optimization
The cross-entropy and minimum cross-entropy methods are well-known Monte Carlo simulation techniques for rare-event probability estimation and optimization. In this paper, we investigate how these methods can be extended to provide a general non-parametric cross-entropy framework based on 1-divergence distance measures. We show how the 2 2 distance, in particular, yields a viable alternative to...
متن کاملOn Generalized Exponential Fuzzy Entropy
In the present communication, the existing measures of fuzzy entropy are reviewed. A generalized parametric exponential fuzzy entropy is defined.Our study of the four essential and some other properties of the proposed measure, clearly establishes the validity of the measure as an entropy. Keywords—fuzzy sets, fuzzy entropy, exponential entropy, exponential fuzzy entropy.
متن کاملOn Applications of a Generalized Hyperbolic Measure of Entropy
After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s) from application point of view? In the pre...
متن کامل