Article
Mathematics, Interdisciplinary Applications
Keqiang Dong, Shushu Li, Dan Li
Summary: This paper first introduces the properties of fractional cumulative residual entropy (FCRE), and then extends cumulative residual entropy (CRE) to the case of conditional entropy, proposing fractional conditional cumulative residual entropy (FCCRE) and discussing its properties. The validity of these properties is verified using randomly generated sequences with different distributions. Additionally, the definition of empirical fractional conditional accumulative residual entropy is given, and it is proven that it can be used to approximate FCCRE. Finally, an empirical analysis is conducted on aero-engine gas path data, showing that FCRE and FCCRE can effectively capture complex information in the gas path system.
FRACTAL AND FRACTIONAL
(2022)
Article
Physics, Multidisciplinary
Mohamed Kayid, Mansour Shrahili
Summary: This paper investigates the properties of fractional cumulative entropy and its developments in dynamic cases. It also explores the connections between this measure and classical differential entropy, as well as some reliability quantities. Furthermore, the association between the measure and standard deviation is discovered. Several examples are provided to demonstrate the variability property of this measure.
Article
Physics, Multidisciplinary
Sudheesh Kumar Kattumannil, E. P. Sreedevi, Narayanaswamy Balakrishnan
Summary: In this paper, a generalized measure of cumulative residual entropy is introduced and its properties are studied. Relationships between different measures of entropy and extropy are established.
Article
Computer Science, Interdisciplinary Applications
Muhammed Sutcu
Summary: In this paper, an alternative formulation of utility entropy called disutility entropy is presented to overcome the inability to apply utility entropy in cases with multiple attributes. By using multiattribute utility functions, the entropy measurement is simplified and the usefulness and feasibility of the method in the field of multiattribute utility theory are improved.
COMPUTERS & INDUSTRIAL ENGINEERING
(2022)
Article
Physics, Multidisciplinary
Omid Kharazmi, Narayanaswamy Balakrishnan, Hassan Jamali
Summary: In this paper, we define cumulative residual q-Fisher and chi-square divergence measures and investigate their connections with related functions. The properties and inter-connections of these measures are discussed, and numerical results for a real example are provided.
Article
Mathematics, Applied
N. Unnikrishnan Nair, S. M. Sunoj, B. Vineshkumar
Summary: The paper investigates the fundamental concepts of information and its measurement in statistical analysis. It explores the use of cumulative residual entropy instead of the traditional Shannon measure. The Bayes information measure is derived and illustrated through specific models and simulated samples.
RICERCHE DI MATEMATICA
(2023)
Article
Mathematics, Interdisciplinary Applications
Keqiang Dong, Shushu Li
Summary: Mean relative entropy is widely used in measuring information differences. However, approximating relative entropy from empirical distribution entropy is challenging. To address this, we introduce the fractional-order cumulative residual mean relative entropy, which replaces the probability density function with the residual distribution function and incorporates fractional-order calculation. This new entropy can be approximated by the empirical entropy of sample data and provides detailed information about the underlying system. Statistical properties are analyzed, and convergence to theoretical values is shown. Finally, this entropy is applied to analyze aeroengine gas path data.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Information Systems
Omid Kharazmi, Narayanaswamy Balakrishnan
Summary: In this work, new measures of cumulative residual Fisher information and relative cumulative residual Fisher information were proposed, and their properties were established. These measures were expressed based on hazard functions and Jensen inequality, with discussions on connections between different information measures using a new version of de Bruijn's identity for survival functions.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Mathematics, Applied
Abdolsaeed Toomaj
Summary: In this paper, a new measure of dispersion called the generalized cumulative residual Tsallis entropy is introduced and its properties are thoroughly investigated. The findings highlight the unique properties and potential applications of the new measure.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Ghadah Alomani, Mohamed Kayid
Summary: This paper investigates new results for the fractional generalized cumulative residual entropy (FGCRE), including its representations and bounds derivation, as well as its connections with stochastic orders and reliability measures. It is proved that FGCRE is the Bayesian risk of mean residual lifetime (MRL), and the normalized version and its connection with the Lorenz curve ordering are studied.
Article
Physics, Multidisciplinary
Mohamed Kayid, Mashael A. Alshehri
Summary: Recently, there has been increasing interest in alternative measures of uncertainty, such as cumulative residual entropy. This paper investigates the cumulative residual entropy of mixed systems and explores its expressions, limits, and order properties. The study also proposes a criterion based on relative residual cumulative entropy for selecting the best system configuration. These findings provide valuable insights into the predictability of mixed systems and have practical applications in various fields.
Article
Computer Science, Artificial Intelligence
Zhuo Wang, Pengjian Shang, Xuegeng Mao
Summary: In this paper, the cumulative residual Tsallis singular entropy (CRTSE) is introduced to measure the complex characteristics of nonlinear signals. The effectiveness and robustness of CRTSE are verified through simulation experiments. The proposed CRTSE-GWOSVM model based on grey wolf optimized support vector machine (GWOSVM) can effectively and accurately identify complex systems.
EXPERT SYSTEMS WITH APPLICATIONS
(2024)
Article
Mathematics
Marius Giuclea, Costin-Ciprian Popescu
Summary: In this paper, we investigate two generalizations of the Lindley distribution and explore their special properties related to the geometric mean and the cumulative residual entropy. Both properties are of great importance from both theoretical and practical perspectives.
Article
Physics, Multidisciplinary
Muhammed Rasheed Irshad, Radhakumari Maya, Francesco Buono, Maria Longobardi
Summary: This paper proposes non-parametric kernel estimators for CRTE and DCRTE, and establishes the asymptotic properties of the estimators under suitable regularity conditions. The proposed estimators are evaluated numerically and through Monte Carlo simulations.
Article
Mathematics, Applied
Abdolsaeed Toomaj, Habibollah Agh Atabay
Summary: This paper introduces some further results related to the cumulative residual Tsallis entropy, including new equivalent expressions, bounds, normalized CRTE, and its connection to the differential entropy and excess wealth transform. Additionally, the problem of estimating CRTE using empirical CRTE is discussed, and practical results in blind image quality assessment are studied.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Muhammed Sutcu
Summary: In this paper, an alternative formulation of utility entropy called disutility entropy is presented to overcome the inability to apply utility entropy in cases with multiple attributes. By using multiattribute utility functions, the entropy measurement is simplified and the usefulness and feasibility of the method in the field of multiattribute utility theory are improved.
COMPUTERS & INDUSTRIAL ENGINEERING
(2022)
Article
Computer Science, Artificial Intelligence
Baris Yildiz, Muhammed Sutcu
Summary: This paper examines a selling environment in which a manufacturer-controlled retailer and an independent retailer sell a slow-moving A item. By offering price protection contracts and implementing pricing strategies, as well as considering customer preferences and the no-purchase option, the study investigates the impact on metrics such as price, market shares, and expected profits.
EXPERT SYSTEMS WITH APPLICATIONS
(2023)
Proceedings Paper
Physics, Applied
Muhammed Sutcu, Ali E. Abbas
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING (MAXENT 2014)
(2015)