Related papers: Varentropy of past lifetimes
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
This study explores information measures based on extropy, introducing dynamic relative extropy measures for residual and past lifetimes, and investigating their various properties. Furthermore, the study analyzes the relationships between…
Shannon entropy is widely used to quantify the uncertainty of discrete random variables. But when normalized to the unit interval, as is often done in practice, it no longer conveys the alphabet sizes of the random variables being studied.…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The…
We consider the evolution of variance of entropy (varentropy) in the course of a polar transform operation on binary data elements (BDEs). A BDE is a pair $(X,Y)$ consisting of a binary random variable $X$ and an arbitrary side information…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…
Entropic measures of complexity are able to quantify the information encoded in complex network structures. Several entropic measures have been proposed in this respect. Here we study the relation between the Shannon entropy and the Von…
Volcanic regions have shaped human settlements for millennia, placing over 500 million people worldwide within close proximity to active volcanoes. Predicting eruptions that threaten both lives and property remains a critical challenge,…
Number-phase uncertainty relations are formulated in terms of unified entropies which form a family of two-parametric extensions of the Shannon entropy. For two generalized measurements, unified-entropy uncertainty relations are given in…
Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure…
We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…
As data plays an increasingly pivotal role in decision-making, the emergence of data markets underscores the growing importance of data valuation. Within the machine learning landscape, Data Shapley stands out as a widely embraced method…
Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed…
Shannon entropy is not the only entropy that is relevant to machine-learning datasets, nor possibly even the most important one. Traditional entropies such as Shannon entropy capture information represented by elements' frequencies but not…
In this paper, we propose nonparametric estimators for varextropy function of an absolutely continuous random variable. Consistency of the estimators is established under suitable regularity conditions. Moreover, a simulation study is…
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…
We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the…