Related papers: Interval extropy and weighted interval extropy
In Reliability Theory, uncertainty is measured by the Shannon entropy. Recently, in order to analyze the variability of such measure, varentropy has been introduced and studied. In this paper we define a new concept of varentropy for past…
In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are…
We introduce two uncertainty measures, say weighted past varentropy (WPVE) and weighted paired dynamic varentropy (WPDVE). Several properties of these proposed measures, including their effect under the monotone transformations are studied.…
In this paper, we investigate several properties of the weighted varextropy measure and obtain it for specific distribution functions, such as the equilibrium and weighted distributions. We also obtain bounds for the weighted varextropy, as…
Weighted extropy has recently emerged as a flexible information measure for quantifying uncertainty, with particular relevance to order statistics. In this paper, we introduce and study a weighted cumulative analogue of extropy, extending…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
In information theory, it is of recent interest to study variability of the uncertainty measures. In this regard, the concept of varentropy has been introduced and studied by several authors in recent past. In this communication, we study…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative extropy are…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
In the recent information-theoretic literature, the concept of extropy has been studied for order statistics. In the present communication we consider a cumulative analogue of extropy in the same vein of cumulative residual (past) entropy…
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…
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…
In Basili and Pratelli (2024), a novel and coherent concept of interval probability measures has been introduced, providing a method for representing imprecise probabilities and uncertainty. Within the framework of set algebra, we…
This paper introduces and studies a new uncertainty measure, the cumulative residual interval entropy (CRIE). Defined as the cumulative residual entropy of a doubly truncated (interval) continuous random variable, this measure has several…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class…
We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…