On characterization of useful information-theoretic measures
On dimensions of semimetrized measure spaces
On dispersion measures.
In this paper a new framework for the study of measures of dispersion for a class of n-dimensional lists is proposed. The concept of monotonicity with respect to a sharpened-type order is introduced. This type of monotonicity, together with other well known conditions, allows to create a reasonable and general ambit where the notion of dispersion measure can be studied. Some properties are analized and relations with other approaches carried out by different authors on this subject are established....
On entropies for random partitions of the unit segment
We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.
On entropy-like functionals and codes for metrized probability spaces. I.
On entropy-like functionals and codes for metrized probability spaces II
In Part I, we have proved characterization theorems for entropy-like functionals , , , and restricted to the class consisting of all finite spaces , the class of all semimetric spaces equipped with a bounded measure. These theorems are now extended to the case of , and defined on the whole of , and of and restricted to a certain fairly wide subclass of .
On extended Shannon entropies and the epsilon entropy
On Fisher information inequalities and score functions in non-invertible linear systems.
On generalized conditional cumulative past inaccuracy measure
The notion of cumulative past inaccuracy (CPI) measure has recently been proposed in the literature as a generalization of cumulative past entropy (CPE) in univariate as well as bivariate setup. In this paper, we introduce the notion of CPI of order and study the proposed measure for conditionally specified models of two components failed at different time instants, called generalized conditional CPI (GCCPI). Several properties, including the effect of monotone transformation and bounds of GCCPI...
On generalized entropies, Bayesian decisions and statistical diversity
On generalized information and divergence measures and their applications: a brief review.
The aim of this review is to give different two-parametric generalizations of the following measures: directed divergence (Kullback and Leibler, 1951), Jensen difference divergence (Burbea and Rao 1982 a,b; Rao, 1982) and Jeffreys invariant divergence (Jeffreys, 1946). These generalizations are put in the unified expression and their properties are studied. The applications of generalized information and divergence measures to comparison of experiments and the connections with Fisher information...
On generalized measures of relative information and inaccuracy
Kullback's relative information and Kerridge's inaccuracy are two information-theoretic measures associated with a pair of probability distributions of a discrete random variable. The authors study a generalized measure which in particular contains a parametric generalization of relative information and inaccuracy. Some important properties of this generalized measure along with an inversion theorem are also studied.
On (..., k)-Normal Words in Connecting Dynamical Systems.
On limiting towards the boundaries of exponential families
This work studies the standard exponential families of probability measures on Euclidean spaces that have finite supports. In such a family parameterized by means, the mean is supposed to move along a segment inside the convex support towards an endpoint on the boundary of the support. Limit behavior of several quantities related to the exponential family is described explicitly. In particular, the variance functions and information divergences are studied around the boundary.
On -dimensional unified -Jensen difference divergence measures and their applications
On measurable solutions of a functional equation and its application to information theory
On measurable solutions of a functional equation and their application to information theory
In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon’s entropy and entropy of type is given.
On measures of relative ‘useful’ information
On metric divergences of probability measures
Standard properties of -divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of -divergences, or the metricity of their powers. This paper extends the previously known family of -divergences with these properties. The extension consists of a continuum of -divergences which are squared metric distances and which are mostly new but include...
On probability of first order formulas in a given model