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We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…
Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure.…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…
The paper presents an extension of Shannon fuzzy entropy for intuitionistic fuzzy one. Firstly, we presented a new formula for calculating the distance and similarity of intuitionistic fuzzy information. Then, we constructed measures for…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
Using different extropies of k record values various characterizations are provided for continuous symmetric distributions. The results are in addition to the results of Ahmadi, J. (Statistical Papers, 2021, 62:2603-2626). These include…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
Completely random measures (CRMs) and their normalizations are a rich source of Bayesian nonparametric priors. Examples include the beta, gamma, and Dirichlet processes. In this paper we detail two major classes of sequential CRM…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…