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Objective Bayesian point and region estimation in location-scale models.

José M. Bernardo (2007)

SORT

Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this...

On generalized conditional cumulative past inaccuracy measure

Amit Ghosh, Chanchal Kundu (2018)

Applications of Mathematics

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 α 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 information and divergence measures and their applications: a brief review.

Inder Jeet Taneja, Leandro Pardo, Domingo Morales, María Luisa Menéndez (1989)

Qüestiió

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 limiting towards the boundaries of exponential families

František Matúš (2015)

Kybernetika

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 metric divergences of probability measures

Igor Vajda (2009)

Kybernetika

Standard properties of φ -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 φ -divergences, or the metricity of their powers. This paper extends the previously known family of φ -divergences with these properties. The extension consists of a continuum of φ -divergences which are squared metric distances and which are mostly new but include...

On stochastic properties of past varentropy with applications

Akash Sharma, Chanchal Kundu (2024)

Applications of Mathematics

To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy....

On the amount of information resulting from empirical and theoretical knowledge.

Igor Vajda, Arnost Vesely, Jana Zvarova (2005)

Revista Matemática Complutense

We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 0). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic approach...

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