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Search Results (6)

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Keywords = dynamic cumulative past entropy

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18 pages, 1223 KiB  
Article
Entropy in the Assessment of the Labour Market Situation in the Context of the Survival Analysis Methods
by Beata Bieszk-Stolorz
Entropy 2025, 27(7), 665; https://doi.org/10.3390/e27070665 - 21 Jun 2025
Viewed by 222
Abstract
Since Shannon’s pioneering work, the concept of entropy has been used in many major scientific fields. It is therefore a universal concept but also defined in different ways. Entropy is used in studies of system complexity and to investigate the information content of [...] Read more.
Since Shannon’s pioneering work, the concept of entropy has been used in many major scientific fields. It is therefore a universal concept but also defined in different ways. Entropy is used in studies of system complexity and to investigate the information content of probability distributions. One of the areas of its applications is human lifespan, i.e., the link between entropy and the methods of survival analysis. These methods are also used in assessing the duration of any socio-economic phenomenon. The aim of this article is to assess the market situation on the basis of the entropy of duration in unemployment. This study determines the Shannon entropy, residual entropy, past entropy, and cumulative residual entropy under the assumption of an exponential distribution of duration. Ward’s hierarchical clustering and the Dynamic Time Warping measure were used to analyse entropy and its relationship with the unemployment rate. It was shown that not all of the analysed models determine the entropy of duration in unemployment well for an exponential distribution. It was substantiated that there is a similarity between the formation of the entropy of duration in unemployment and the registered unemployment rate. It is shown that high unemployment rates in the labour market are a destabilising element of the labour market, more so than crises. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Economics, Finance and Management, 3rd Edition)
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30 pages, 444 KiB  
Article
Weighted Mean Inactivity Time Function with Applications
by Antonio Di Crescenzo and Abdolsaeed Toomaj
Mathematics 2022, 10(16), 2828; https://doi.org/10.3390/math10162828 - 9 Aug 2022
Cited by 1 | Viewed by 1861
Abstract
We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, [...] Read more.
We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, the past entropy, the varentropy, and the weighted cumulative entropy. Moreover, based on the comparison of weighted mean inactivity times, we introduce and study a new stochastic order and compare it with other suitable orders. We also discuss some results about the variance of transformed random variables and the weighted generalized cumulative entropy. Then, we investigate certain connections with the location-independent riskier order. Finally, we pinpoint several characterizations and preservation properties of the new stochastic order under shock models, random maxima, and notions of renewal theory. Full article
(This article belongs to the Special Issue Mathematics: 10th Anniversary)
21 pages, 38225 KiB  
Article
Assessing Variations in Water Use Efficiency and Linkages with Land-Use Changes Using Three Different Data Sources: A Case Study of the Yellow River, China
by Huaiwei Sun, Lin Chen, Yong Yang, Mengge Lu, Hui Qin, Bingqian Zhao, Mengtian Lu, Jie Xue and Dong Yan
Remote Sens. 2022, 14(5), 1065; https://doi.org/10.3390/rs14051065 - 22 Feb 2022
Cited by 10 | Viewed by 2955
Abstract
The dependence of water use efficiency (WUE) on changes in land cover types is crucial for understanding of long-term water availability and assessment of water-saving strategies. Investigating the impact of land cover types on ecosystem WUE has important implications when revealing water dynamics [...] Read more.
The dependence of water use efficiency (WUE) on changes in land cover types is crucial for understanding of long-term water availability and assessment of water-saving strategies. Investigating the impact of land cover types on ecosystem WUE has important implications when revealing water dynamics and land management. However, the determination of WUE and its dominant factors have always been subject to high data dependency and large calculation consumption within large basins. This paper proposes a framework for processing actual evapotranspiration (AET) and WUE calculation by coupling the Maximum Entropy Production (MEP) method with the Google Earth Engine (GEE). By employing the proposed framework and three data sources available in the GEE platform, results for actual ET and WUE from 2001 to 2020 were obtained in the Yellow River Basin (YRB). The results show that the proposed framework provides an acceptable estimation of actual ET via validation with Eddy Covariance flux sites in the YRB. The calculated WUE values varied greatly in different sub-basins within the YRB, indicating a cumulative growth rate of about 56% during the past 20 years. The dominant factor that led to these changes was the transition from Grasslands into other land-use types. Our results suggest that the use of the GEE platform coupled with the MEP method offers new possibilities for advancing understanding of water exchange and water resource management. Full article
(This article belongs to the Special Issue Remote Sensing in Agricultural Hydrology and Water Resources Modeling)
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22 pages, 851 KiB  
Article
On the Dynamic Cumulative Past Quantile Entropy Ordering
by Haiyan Wang, Diantong Kang and Lei Yan
Symmetry 2021, 13(11), 2001; https://doi.org/10.3390/sym13112001 - 22 Oct 2021
Cited by 2 | Viewed by 1572
Abstract
In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that [...] Read more.
In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models. Full article
19 pages, 833 KiB  
Article
Further Results on the IDCPE Class of Life Distributions
by Haiyan Wang, Diantong Kang and Lei Yan
Symmetry 2021, 13(10), 1964; https://doi.org/10.3390/sym13101964 - 18 Oct 2021
Viewed by 1672
Abstract
Navarro et al. (2010) proposed the increasing dynamic cumulative past entropy (IDCPE) class of life distributions. In this paper, we investigate some characterizations of this class. Closure and reversed closure properties of the IDCPE class are obtained. As applications of a main result, [...] Read more.
Navarro et al. (2010) proposed the increasing dynamic cumulative past entropy (IDCPE) class of life distributions. In this paper, we investigate some characterizations of this class. Closure and reversed closure properties of the IDCPE class are obtained. As applications of a main result, we explore the preservation and reversed preservation properties of this class in several stochastic models. We also investigate preservation and reversed preservation of the IDCPE class for coherent systems with dependent and identically distributed components. Full article
19 pages, 2737 KiB  
Article
A Shift-Dependent Measure of Extended Cumulative Entropy and Its Applications in Blind Image Quality Assessment
by Saeid Tahmasebi, Ahmad Keshavarz, Maria Longobardi and Reza Mohammadi
Symmetry 2020, 12(2), 316; https://doi.org/10.3390/sym12020316 - 23 Feb 2020
Cited by 6 | Viewed by 2970
Abstract
Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with [...] Read more.
Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy (ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past version. These results contain stochastic order, upper and lower bounds, the symmetry property and some relationships with other reliability functions. We also discuss some properties of conditional weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new measure and study its practical results in blind image quality assessment. Full article
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