Related papers: On relative weighted entropies with central moment…
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…
We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted…
In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…
This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…
In this paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\alpha$-th generalized derivation and ($\alpha$; p)-th weighted Fisher…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
Recently, M. Tsukamoto (New approach to weighted topological entropy and pressure, Ergod. Theory Dyn. Syst. 43 (2023) 1004-1034) used a new approach to define the weighted topological entropy and pressure. Inspired by his ideas, we…
Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
Measure of the weighted cumulative entropy about the predictability of failure time of a system have been introduced in [3]. Referring properties of doubly truncated (interval) cumulative residual and past entropy, several bounds and…
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…
We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
Relative entropy, as a divergence metric between two distributions, can be used for offline change-point detection and extends classical methods that mainly rely on moment-based discrepancies. To build a statistical test suitable for this…
In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability…
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…
The notion of weighted Renyi's entropy for truncated random variables has recently been proposed in the information-theoretic literature. In this paper, we introduce a generalized measure of it for double truncated distribution, namely…
The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under…