Although numerous studies have looked at the long‐term trend of the temporal variability of winter temperature and precipitation in southern Quebec, no study has focused on the shifts in series means and the dependence between these two types of climate variables associated with this long‐term trend. To fill these gaps, we used the Lombard method to detect the shifts in mean values and the copula method to detect any change in dependence between extreme (maximum and minimum) temperatures and precipitation (snow and rain) over the periods 1950–2000 (17 stations) and 1950–2010 (7 stations). During these two periods, the shifts in mean values of temperature and precipitation were recorded at less than half of the stations. The only significant change observed at the provincial scale is a decrease in the amount of snowfall, which occurred in many cases during the 1970s. This decrease affected stations on the north shore (continental temperate climate) more strongly than stations on the south shore (maritime temperate climate) of the St Lawrence River. However, this decrease in the amount of snowfall had no impact on the dependence over time between temperature and precipitation as snow.

This paper explores the properties of a family of bivariate copulas based on a new approach using the counter-monotonic shock method. The resulting copula covers the full range of negative dependence induced by one parameter. Expressions for the copula and density are derived and many theoretical properties are examined thoroughly, including explicit expressions for prominent measures of dependence, namely Spearman’s rho, Kendall’s tau and Blomqvist’s beta. The convexity properties of this copula are presented, together with explicit expressions of the mixed moments. Estimation of the dependence parameter using the method of moments is considered, then a simulation study is carried out to evaluate the performance of the suggested estimator. Finally, an application of the proposed copula is illustrated by means of a real data set on air quality in New York City.

The measurement of uncertainty across the lifetimes of engineering systems has drawn more attention in recent years. It is a helpful metric for assessing how predictable a system’s lifetime is. In these circumstances, Renyi entropy, a Shannon entropy extension, is particularly appealing. In this paper, we develop the system signature to give an explicit formula for the Renyi entropy of the residual lifetime of a coherent system when all system components have lived to a time t. In addition, several findings are studied for the aforementioned entropy, including the bounds and order characteristics. It is possible to compare the residual lifespan predictability of two coherent systems with known signatures using the findings of this study.

The Vehicle-to-Grid (V2G) networks are a part of the Smart Grid networks. Their primary goal is to recharge electric vehicles. These networks, as with any computer system, are facing cyber attacks. For example, during a charge or recharge process, V2G networks can be vulnerable to attacks such as Man-in-the-Middle (MitM), Denial of Service (DoS), identity theft, and rebound attacks. It is therefore up to us to offer innovative solutions in order to reduce threats as much as possible. In this paper, a model based on copulas to detect intrusion cases in V2G networks is proposed. To achieve this model, a database is generated first from three scenarios using tools including MiniV2G, Wireshark, and CICflowMeter. Then, significant variables are selected using Principal Component Analysis (PCA). The classification algorithm is based on the notion of copulas constructed under the software R. From the obtained results, it emerges that the created model has a very high prediction rate of attacks in the aforementioned network.

In order to protect stakeholders of insurance companies and financial institutions against adverse outcomes of risky businesses, regulators and senior management use capital allocation techniques. For enterprise-wide risk management, it has become important to calculate the contribution of each risk within a portfolio. For that purpose, bivariate lower and upper orthant tail value-at-risk can be used for capital allocation. In this paper, we present multivariate value-at-risk and tail-value-at-risk for $d\ge 2$ , and we focus on three different methods to calculate optimal values for the contribution of each risk within the sums of random vectors to the overall portfolio, which could particularly apply to insurance and financial portfolios.

Skellam's name is traditionally attached to the distribution of the difference of two independent Poisson random variables. Many bivariate extensions of this distribution are possible, e.g., through copulas. In this paper, the authors focus on a probabilistic construction in which two Skellam random variables are affected by a common shock. Two different bivariate extensions of the Skellam distribution stem from this construction, depending on whether the shock follows a Poisson or a Skellam distribution. The models are nested, easy to interpret, and yield positive quadrant-dependent distributions, which share the convolution closure property of the univariate Skellam distribution. The models can also be adapted readily to account for negative dependence. Closed form expressions for Pearson's correlation between the components make it simple to estimate the para-meters via the method of moments. More complex formulas for Kendall's tau and Spearman's rho are also provided.