In this paper, in order to calculate portfolio market risk of 10 selected industries indices in Tehran Stock Exchange, two models of Value Risk (VaR) and Expected shortfall (ES) have been used. Different models of multivariate GARCH and various Coppola models have been used in order to estimate the volatility of the portfolio and nonlinear correlation of asset portfolio. Backtesting has been done by Kupiec, Christoffersen, Engle and Manganelli and McNeill and Ferry tests. Results show that the DCC-GARCH model by t-Student distribution compared to other competing models has the best results in estimating volatility of the asset portfolio. Also among all Copula models reviewed in this paper, t-student Copula model has shown better results for estimating asset dependence. Finally, the results of backtesting of different models showed that both the DCC-GARCH model with t-Student distribution and DCC-GARCH-Copula with t-Student distribution have acceptable results in estimating VaR and ES. However, the Lopez and Blanco and Ihle tests showed that the DCC-GARCH model with t-Student distribution compared to the DCC-GARCH-Copula model with t-Student distribution gives a more accurate and efficient estimate of the VaR and ES of asset portfolios.

In this work, we study the joint distribution function as well as the Copula of (X-Z; Y ) where the random vector (X; Y; Z) is characterized by a Copula CX; Y; Z. We use this Copula to analyze a measurement error model. Some theoretical results, several examples as well as a simulation study are proposed for illustration.

In applications of differential geometry to problems of parametric inference, the notion of divergence is often used to measure the separation between two parametric densities. Among them, in this paper, we will verify measures such as Kullback-Leibler information, J-divergence, Hellinger distance, a -Divergence, ... and so on. Properties and results related to distance between probability distributions derived via Copula functions. Some inequalities are obtained in view of the dependence and information measures.

In this work, we consider the joint distribution function as well as the Copula of $(X+Z,Y)$ where the random vector $(X, Y, Z)$  is characterized by a Copula $C_{X,Y,Z}$. We use this Copula to analyze a Berkson measurement error model. By presenting a general form of a Berkson measurement error model with Copula-dependent random variables, we investigate some of its special cases. Some theoretical results, several examples as well as a simulation study, are proposed for illustration.

In this paper, we apply R-Vine Copula-ARMA-APGARCH approach to investigate the dynamic relationship between banking, insurance and pension, investment and other financials sub-indexes in Tehran stock exchange. Using a sample of more than 8 years of daily return observations of the financial sub-indexes, we find evidence of significant and symmetric relationship between these variables. Finally, there is evidence to suggest that the application of the vine Copula model improves the accuracy of VaR estimates, compared to traditional approaches. This paper results show that vine Copula VaR is accurate at 1% and 5% significance levels. This paper’ s findings suggest the flexibility and capacity of vine Copula structures in financial dependency modeling and risk management.

Many survival data analyses aim to assess the effect of different risk factors on survival time‎. ‎In some studies‎, ‎the survival times are correlated‎, ‎and the dependence between survival times is related to their spatial locations‎. ‎Identifying and considering the dependence structure of data is essential in survival modeling‎. ‎The Copula functions are helpful tools for incorporating data dependencies‎. ‎So‎, ‎one may use these functions for modelling spatial survival data‎. ‎This paper presents a model for spatial survival data by the Gumbel-Hougaard Copula function‎. ‎A two-stage estimator using a composite likelihood function is used to estimate regression and dependence parameters‎. ‎A simulation study investigates the performance of the model‎. ‎Finally‎, ‎the proposed model is applied to model a set of COVID-19 data.

The purpose of this study is to calculate Value at Risk (VaR) of a selection of bank's currency portfolio, using GARCH- EVT- Copula (GEC) approach. Today's main challenge of a banking system is to calculate and quantify the risks that the system is encountered. There are numerous approaches to calculate the risks. usually these approaches assume a common known distribution for the assets portfolio and generally a normal distribution is utilized for the experimental models. Nevertheless, the distributions of the assets are fat-tailed distribution and consequently normal distribution assumption may lead to inaccurate estimation. This article does not assume a specific asset distribution. This study applies autoregressive threshold variances (GJR- GARCH) for inter temporal individual's asset variable returns distribution. It also utilizes extreme value theory or the fat-tailed distributions and Coppola functions for all asset returns in an asset portfolio. In this study VaR is estimated using variance- covariance and historical simulation methods. Finally, in order to test the reliability of the applied models Kopic method is used. The sample data of the bank's currency portfolio consists of the market daily figures of the US Dollar, Japan's Yen, Turkish Lire, Emirate Dirham, Korean Won, and Euro exchange rates from 21March 2007 till 19 April 2012. Results show that the estimated VaR using GEC model is higher than those of estimated using the other two methods. They also show that reliability and precision of Kopic test is higher than those of variance-covariance and historical simulation models.

In fuzzy logic, the evaluation of conditional statements is done using implication operators. Implicative operators are two-variable functions on the unit square support and a generalization of the two-valued imputation of classical logic. Various methods have been presented to construct imperative operators. One class of these functions is probabilistic imputations that are built based on detailed functions. In this article, four families of detailed probabilistic implications of the basis are introduced and some inference rules for two families of these operators are studied. Finally, applications of these concepts in medicine, agriculture, and underground water resources are presented.

In the conventional methods of flood frequency analysis, the flood peak variable is just considered and assumed that this variable follows some specific parametric distribution function. This assumption would restrict us and lead us to the limited available information to evaluate the flood risk. It is well known that a flood event has three variables of flood peak, volume and duration which are random in nature and are mutually dependent. In this research, the concept of the Copula function is briefly introduced and then used to modeling the dependency structure of the flood variables of the Karun River at the Ahvaz hydrometric station and then estimate their joint probability distribution. We use three well-known and appropriate Copulas, including Ali–Mikhail–Haq, Cook–Johnson and Gumbel–Hougaard which belong to the Archimedean class of Copulas, to modeling the joint probability distribution of the flood variables, where the marginal distributions of the flood’s variables are selected from the parametric and non-parametric distributions. The Gumbel–Hougaard family led to better modeling of different combination of flood’s variables based on goodness of fit criteria.The selected Copula is used to estimate conditional cumulative distribution function and joint return periods which lead to better estimation of flood risk.