Related papers: Varentropy of past lifetimes
Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability…
Connectedness measures the degree at which a time-series variable spills over volatility to other variables compared to the rate that it is receiving. The idea is based on the percentage of variance decomposition from one variable to the…
The concept of mean inactivity time plays a crucial role in reliability, risk theory and life testing. In this regard, we introduce a weighted mean inactivity time function by considering a non-negative weight function. Based on this…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…
The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
Parametric statistical methods play a central role in analyzing risk through its underlying frequency and severity components. Given the wide availability of numerical algorithms and high-speed computers, researchers and practitioners often…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
Misclassification detection is an important problem in machine learning, as it allows for the identification of instances where the model's predictions are unreliable. However, conventional uncertainty measures such as Shannon entropy do…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…