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Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…

Statistical Mechanics · Physics 2007-05-23 Piotr Garbaczewski

Existing research on negations primarily focuses on entropy and extropy. Recently, new functions such as varentropy and varextropy have been developed, which can be considered as extensions of entropy and extropy. However, the impact of…

Statistics Theory · Mathematics 2025-04-08 Santosh Kumar Chaudhary , Pradeep Kumar Sahu , Nitin Gupta

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…

Quantum Physics · Physics 2007-05-23 C. G. Chakrabarti , Indranil Chakrabarty

Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…

Quantum Physics · Physics 2018-07-04 Shubhayan Sarkar

Recently, Extropy was introduced by Lad, Sanfilippo and Agr\`o as a complement dual of Shannon Entropy. In this paper, we propose dynamic versions of Extropy for doubly truncated random variables as measures of uncertainty called Interval…

Probability · Mathematics 2021-12-03 Francesco Buono , Osman Kamari , Maria Longobardi

Stochastic volatility models describe stock returns $r_t$ as driven by an unobserved process capturing the random dynamics of volatility $v_t$. The present paper quantifies how much information about volatility $v_t$ and future stock…

Mathematical Finance · Quantitative Finance 2016-10-04 Oliver Pfante , Nils Bertschinger

The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…

Statistical Mechanics · Physics 2020-10-28 Qiuping A. Wang

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…

Statistics Theory · Mathematics 2025-07-01 Faranak Goodarzi

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…

Machine Learning · Computer Science 2016-06-09 David Darmon

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Probability · Mathematics 2018-01-23 Alois Pichler , Ruben Schlotter

Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…

Quantum Physics · Physics 2019-05-01 Anaelle Hertz , Nicolas J. Cerf

In the present work, we provide the asymptotic behavior of the residual-past entropy, of the mean residual-past lifetime distribution and of the residual-past inaccuracy measure. We are interested in these measures of uncertainty in the…

Statistics Theory · Mathematics 2019-12-03 Ba Amadou Diadie

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…

Statistical Mechanics · Physics 2025-11-25 Yoshihiko Hasegawa , Tomohiro Nishiyama

The investor is interested in the expected return and he is also concerned about the risk and the uncertainty assumed by the investment. One of the most popular concepts used to measure the risk and the uncertainty is the variance and/or…

Statistical Finance · Quantitative Finance 2008-12-02 Andreia Dionisio , Rui Menezes , Diana A. Mendes

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…

Mathematical Physics · Physics 2010-09-07 Congjie Ou , Aziz El Kaabouchi , Qiuping A. Wang , Jincan Chen

Building on Shannon's lead, let's consider a more malleable expression for tracking uncertainty, and states of "knowledge available" vs. "knowledge missing," to better practice innovation, improve risk management, and successfully measure…

Information Theory · Computer Science 2010-06-08 Gideon Samid

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…

Statistics Theory · Mathematics 2024-01-25 Santosh Kumar Chaudhary , Nitin Gupta

Shannon entropy is the most common metric to measure the degree of randomness of time series in many fields, ranging from physics and finance to medicine and biology. Real-world systems may be in general non stationary, with an entropy…

Statistical Finance · Quantitative Finance 2023-06-08 Andrey Shternshis , Piero Mazzarisi

The traditional measurement theory interprets the variance as the dispersion of a measured value, which is actually contrary to a general mathematical concept that the variance of a constant is 0. This paper will fully demonstrate that the…

Other Statistics · Statistics 2020-09-22 Huisheng Shi , Xiaoming Ye , Cheng Xing , Shijun Ding

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation…

Information Theory · Computer Science 2025-06-17 Masoud Ataei , Xiaogang Wang