Relation Between Cumulative Residual Entropy and Excess Wealth Transform with Applications to Reliability and Risk

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
N. Unnikrishnan Nair ◽  
B. Vineshkumar
Keyword(s):  
Risk Measures ◽  
Real Life ◽  
Residual Entropy ◽  
Information Measures ◽  
Life Data ◽  
Real Life Data ◽  
Cumulative Residual Entropy ◽  
Cumulative Residual ◽  
Theoretical Results

Abstract Dynamic cumulative residual entropy is a new addition to the class of information measures. In the present paper, we study its relationship with excess wealth transform and derive some identities connecting the two using the quantile-based approach. Some theoretical results that have applications to infer ageing properties and risk measures are presented. These are used as tools to analyse real life data.

PROPERTIES FOR GENERALIZED CUMULATIVE PAST MEASURES OF INFORMATION

2018 ◽  
Vol 34 (1) ◽  
pp. 92-111 ◽  
Author(s):  
Camilla Calì ◽  
Maria Longobardi ◽  
Jorge Navarro
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Survival Function ◽  
Residual Entropy ◽  
Coherent Systems ◽  
Underlying Distribution ◽  
Information Measures ◽  
Cumulative Residual Entropy ◽  
Past Entropy ◽  
Cumulative Residual

AbstractThe Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.

A CUMULATIVE RESIDUAL INACCURACY MEASURE FOR COHERENT SYSTEMS AT COMPONENT LEVEL AND UNDER NONHOMOGENEOUS POISSON PROCESSES

2020 ◽  
pp. 1-26
Author(s):  
Vanderlei da Costa Bueno ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Reliability Theory ◽  
Poisson Processes ◽  
Residual Entropy ◽  
Coherent Systems ◽  
Component Level ◽  
Martingale Approach ◽  
Information Measures ◽  
Cumulative Residual Entropy ◽  
Nonhomogeneous Poisson Processes ◽  
Cumulative Residual

Inaccuracy and information measures based on cumulative residual entropy are quite useful and have attracted considerable attention in many fields including reliability theory. Using a point process martingale approach and a compensator version of Kumar and Taneja's generalized inaccuracy measure of two nonnegative continuous random variables, we define here an inaccuracy measure between two coherent systems when the lifetimes of their common components are observed. We then extend the results to the situation when the components in the systems are subject to failure according to a double stochastic Poisson process.

scholarly journals Higher-Order Information Measures from Cumulative Densities in Continuous Variable Quantum Systems

2020 ◽  
Vol 2 (4) ◽  
pp. 560-578
Author(s):  
Saúl J. C. Salazar ◽  
Humberto G. Laguna ◽  
Robin P. Sagar
Keyword(s):  
Continuous Variable ◽  
Quantum Systems ◽  
Higher Order ◽  
Residual Entropy ◽  
Information Measures ◽  
Cumulative Residual Entropy ◽  
Interacting Systems ◽  
Correlation Measures ◽  
Cumulative Residual ◽  
Definition Of

A definition of three-variable cumulative residual entropy is introduced, and then used to obtain expressions for higher order or triple-wise correlation measures, that are based on cumulative residual densities. These information measures are calculated in continuous variable quantum systems comprised of three oscillators, and their behaviour compared to the analogous measures from Shannon information theory. There is an overall consistency in the behaviour of the newly introduced measures as compared to the Shannon ones. There are, however, differences in interpretation, in the case of three uncoupled oscillators, where the correlation is due to wave function symmetry. In interacting systems, the cumulative based measures are shown in order to detect salient features, which are also present in the Shannon based ones.

Neuropsychology in the Real World

2014 ◽  
Vol 25 (4) ◽  
pp. 233-238 ◽  
Author(s):  
Martin Peper ◽  
Simone N. Loeffler
Keyword(s):  
Neuropsychological Assessment ◽  
Real World ◽  
Ecological Validity ◽  
Real Life ◽  
Emotional States ◽  
Context Sensitive ◽  
Traditional Assessment ◽  
Life Data ◽  
Real Life Data ◽  
Assessment And Treatment

Current ambulatory technologies are highly relevant for neuropsychological assessment and treatment as they provide a gateway to real life data. Ambulatory assessment of cognitive complaints, skills and emotional states in natural contexts provides information that has a greater ecological validity than traditional assessment approaches. This issue presents an overview of current technological and methodological innovations, opportunities, problems and limitations of these methods designed for the context-sensitive measurement of cognitive, emotional and behavioral function. The usefulness of selected ambulatory approaches is demonstrated and their relevance for an ecologically valid neuropsychology is highlighted.

The epidemiology of thyroid cancer within a center of excellence in Athens: Real life data

2017 ◽  
Author(s):  
Eleni Pantazi ◽  
Alexios Travlos ◽  
Evaggelia Vogiatzi ◽  
Ifigenia Kostoglou-Athanassiou
Keyword(s):  
Thyroid Cancer ◽  
Real Life ◽  
Life Data ◽  
Center Of Excellence ◽  
Real Life Data
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