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This paper deals with preservation of the reversed hazard rate order between equilibrium random variables under formations of some reliability structures. We further investigate a new aging notion based upon the reversed hazard rate order between a random life and its equilibrium version. A nonparametric method is developed to test the exponentiality against such a strict aging property, some numerical results are presented as well. [ABSTRACT FROM AUTHOR]

In this paper, the relative dependence of a linear regression model is studied. In particular, the dependence of autoregressive models in time series are investigated. It is shown that for the first-order non-stationary autoregressive model and the random walk with trend and drift model, the dependence between two states decreases with lag. Some numerical examples are presented as well. [ABSTRACT FROM AUTHOR]

Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative distribution function of the convolutions. Some examples of the practical applications of our results are given. [ABSTRACT FROM AUTHOR]

Bidder asymmetries are common in certain auctions where heterogeneous bidders coexist. In this paper, we employ the tool of majorization to study the effect of bidder asymmetry on revenue in second-price auctions. As a preorder on vectors of real components, the majorization is used to rank the asymmetry of bid distributions from different auctions. Our analysis indicates that bidders' asymmetries may raise revenue under certain classes of value distributions (e.g., proportional reversed hazard rate models) and may not in others (e.g., proportional hazard rate models). These results are further validated through supportive evidence that is based on simulated three-bidder auctions. The use of majorization allows us to extend and strengthen the results obtained in the existing literature under more general conditions. This study adds to the literature a useful analytical technique for future research on asymmetric auctions. [ABSTRACT FROM AUTHOR]

Order statistics from heterogeneous samples have been extensively studied in the literature. However, most of the work focused on the effect of heterogeneity on the magnitude or dispersion of order statistics. In this paper, we study the skewness of order statistics from heterogeneous samples according to star ordering. The main results extend the corresponding results in Kochar and Xu (J. Appl. Probab. 46:342-352, ; J. Appl. Probab. 48:271-284, ). Examples and applications are highlighted as well. [ABSTRACT FROM AUTHOR]

The urban ecosystem possesses dissipating structures that can absorb substances and energy from the external environment and export products and wastes to maintain order within the system. Given these circumstances, this paper analyzed the ability of the urban ecosystem in Guangzhou City to sustain development from the perspective of entropy. The research was carried out in three steps. First, an evaluation index system that considers the ability of the urban ecosystem for sustainable development was formed based on the structures and functions of the urban ecosystem and the change in the entropy of the urban socioeconomic ecosystem. Second, the sustainable development ability assessment model for the urban ecosystem was built using information entropy. Last, by combining the time series variation of the evaluation indicators with the entropy weights, this paper analyzed the influence of the combined factors on the sustainable development ability of the urban ecosystem in Guangzhou and suggested some measures to promote the sustainable development of the urban ecosystem in Guangzhou. The conclusions of this study can be summarized as follows: (1) The urban ecosystem has developed in an orderly and healthy direction, with effective control over the urban environmental pollution problems in Guangzhou between 2004 and 2010. (2) The sustainable development ability of the urban ecosystem had been on an upward trend in Guangzhou during the study period. The ability of the natural urban ecosystem to support the urban socioeconomic ecosystem increased continuously, and the improved ecoenvironment enhanced the harmony and vitality of the urban ecosystem in Guangzhou. [ABSTRACT FROM AUTHOR]

Like how useful weather forecasting is, the capability of forecasting or predicting cyber threats can never be overestimated. Previous investigations show that cyber attack data exhibits interesting phenomena, such as long-range dependence and high nonlinearity, which impose a particular challenge on modeling and predicting cyber attack rates. Deviating from the statistical approach that is utilized in the literature, in this paper we develop a deep learning framework by utilizing the bi-directional recurrent neural networks with long short-term memory, dubbed BRNN-LSTM. Empirical study shows that BRNN-LSTM achieves a significantly higher prediction accuracy when compared with the statistical approach. [ABSTRACT FROM AUTHOR]