Weighted cumulative entropy and its estimation

The generalized cumulative residual entropy is a recently defined dispersion measure. In this paper, we obtain some further results for such a measure, in relation to the generalized cumulative residual entropy and the variance of random lifetimes. We show that it has an intimate connection with the non-homogeneous Poisson process. We also get new expressions, bounds and stochastic comparisons involving such measures. Moreover, the dynamic version of the mentioned notions is studied through the residual lifetimes and suitable aging notions. In this framework we achieve some findings of interest in reliability theory, such as a characterization for the exponential distribution, various results on k-out-of-n systems, and a connection to the excess wealth order. We also obtain similar results for the generalized cumulative entropy, which is a dual measure to the generalized cumulative residual entropy.

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Weighted general cumulative entropy and a goodness of fit for normality

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2020.1723635 ◽

2020 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Sangun Park

Keyword(s):

Goodness Of Fit ◽

Cumulative Entropy

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A MODIFIED MCDM ALGORITHM WITH CUMULATIVE ENTROPY WEIGHTS FOR SELECTING THE WINNER OF THE TENDER

Strategic decisions and risk management ◽

10.17747/2618-947x-2019-1-46-51 ◽

2019 ◽

pp. 46-51

Author(s):

A. O. Matin ◽

F. Misagh

Keyword(s):

Decision Making ◽

Evaluation Criteria ◽

Specific Weight ◽

Multi Criteria Decision Making ◽

Efficient Management ◽

Research Findings ◽

Utility Rate ◽

Input Variables ◽

Decision Making Model ◽

Cumulative Entropy

The aim of this research is to evaluate the proposed bids using impartial and entropy weights in a multi-criteria decision-making model. We use matrix data for hypothetical bidding involving nine criteria, with the presence of four domestic and two foreign contractors. Then, using cumulative entropy function, we estimate the entropy weights and use it in a multi-criteria decision-making model. The criteria of experience and knowledge in the field, good history and satisfaction in previous projects, financial and support capabilities, localization of the contractor, having the experience at the site of the project, availability and readiness of equipment and machines, the adequacy of technical staff, the work quality system, the efficient management and appropriate management system, creativity and innovation in similar tasks are the input variables of the decision model. After analyzing them, the proposals are prioritized through a multi-criteria decision-making model. The research findings include Shannon entropy and cumulative entropy-based weights for evaluation criteria and after applying the specific weight for the proposed quotation, the utility rate of each contractor is calculated. The results showed that the use of modified multi-dimensional decision-making method is more advantageous than traditional methods of evaluating bidding proposals in selecting the winner of a tender, and also using cumulative entropy weights in comparison with Shannon's leads to a more realistic choice of contractors.

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Nonuniform Sparse Data Clustering Cascade Algorithm Based on Dynamic Cumulative Entropy

Mathematical Problems in Engineering ◽

10.1155/2016/5707692 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10

Author(s):

Ning Li ◽

Yunxia Gu ◽

Zhongliang Deng

Keyword(s):

Initial Data ◽

Prior Knowledge ◽

Clustering Algorithm ◽

Sparse Data ◽

Cluster Center ◽

Control Factor ◽

Cascade Algorithm ◽

Initial Cluster ◽

Data Clusters ◽

Cumulative Entropy

A small amount of prior knowledge and randomly chosen initial cluster centers have a direct impact on the accuracy of the performance of iterative clustering algorithm. In this paper we propose a new algorithm to compute initial cluster centers for k-means clustering and the best number of the clusters with little prior knowledge and optimize clustering result. It constructs the Euclidean distance control factor based on aggregation density sparse degree to select the initial cluster center of nonuniform sparse data and obtains initial data clusters by multidimensional diffusion density distribution. Multiobjective clustering approach based on dynamic cumulative entropy is adopted to optimize the initial data clusters and the best number of the clusters. The experimental results show that the newly proposed algorithm has good performance to obtain the initial cluster centers for the k-means algorithm and it effectively improves the clustering accuracy of nonuniform sparse data by about 5%.

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Extension of the past lifetime and its connection to the cumulative entropy

Journal of Applied Probability ◽

10.1017/s0021900200113142 ◽

2015 ◽

Vol 52 (04) ◽

pp. 1156-1174 ◽

Cited By ~ 8

Author(s):

Antonio Di Crescenzo ◽

Abdolsaeed Toomaj

Keyword(s):

Random Variables ◽

Independent Random Variables ◽

Stochastic Orders ◽

Absolutely Continuous ◽

The Past ◽

Probability Densities ◽

The Mean ◽

Weighted Probability ◽

Series Systems ◽

Cumulative Entropy

Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazard rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated.

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Extension of the past lifetime and its connection to the cumulative entropy

Journal of Applied Probability ◽

10.1239/jap/1450802759 ◽

2015 ◽

Vol 52 (4) ◽

pp. 1156-1174 ◽

Cited By ~ 8

Author(s):

Antonio Di Crescenzo ◽

Abdolsaeed Toomaj

Keyword(s):

Random Variables ◽

Independent Random Variables ◽

Stochastic Orders ◽

Absolutely Continuous ◽

The Past ◽

Probability Densities ◽

The Mean ◽

Weighted Probability ◽

Series Systems ◽

Cumulative Entropy

Given two absolutely continuous nonnegative independent random variables, we define the reversed relevation transform as dual to the relevation transform. We first apply such transforms to the lifetimes of the components of parallel and series systems under suitably proportionality assumptions on the hazard rates. Furthermore, we prove that the (reversed) relevation transform is commutative if and only if the proportional (reversed) hazard rate model holds. By repeated application of the reversed relevation transform we construct a decreasing sequence of random variables which leads to new weighted probability densities. We obtain various relations involving ageing notions and stochastic orders. We also exploit the connection of such a sequence to the cumulative entropy and to an operator that is dual to the Dickson-Hipp operator. Iterative formulae for computing the mean and the cumulative entropy of the random variables of the sequence are finally investigated.

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Notes on Cumulative Entropy as a Risk Measure

Stochastics and Quality Control ◽

10.1515/eqc-2018-0019 ◽

2019 ◽

Vol 34 (1) ◽

pp. 1-7

Author(s):

Saeid Tahmasebi ◽

Hojat Parsa

Keyword(s):

Standard Deviation ◽

Stock Market ◽

Risk Measure ◽

Oecd Countries ◽

Mean Difference ◽

Empirical Approach ◽

Differential Entropy ◽

Gini Mean Difference ◽

Cumulative Entropy

Abstract Di Crescenzo and Longobardi [Di Crescenzo and Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 2009, 12, 4072–4087] proposed the cumulative entropy (CE) as an alternative to the differential entropy. They presented an estimator of CE using empirical approach. In this paper, we consider a risk measure based on CE and compare it with the standard deviation and the Gini mean difference for some distributions. We also make empirical comparisons of these measures using samples from stock market in members of the Organization for Economic Co-operation and Development (OECD) countries.

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