One of the methods that in recent years has attracted the attention of many researchers for modeling multivariate mixed outcome data is using the copula function. In this paper a regression model for mixed survival and discrete outcome data based on copula function is proposed. Where the continuous variable was time and could has censored observations. For this task it is assumed that marginal distributions are known and a latent variable was used to transform discrete variable to continuous. Then by using a copula function, the joint distribution of two variables was constructed and finally the obtained model was used to model birth interval data in Ahwaz city in south-west of Iran.

The (n-k+1)-out-of-n systems are important types of coherent systems and have many applications in various areas of engineering. In this paper, the general inactivity time of failed components of (n-k+1)-out-of-n system is studied when the system fails at time t>0. First we consider a parallel system including two exchangeable components and then using Farlie-Gumbel-Morgenstern copula, investigate the behavior of mean inactivity time of failed components of the system. In the next part, (n-k+1)-out-of-n systems with exchangeable components are considered and then, some stochastic ordering properties of the general inactivity time of the systems are presented based on one sample or two samples.

One of the applicable tools, in order to develop the economy's politics, is Iranian's cooperation in increasing their level of public knowledge and the humanization of economic. Economical index, rate, price, and percentage are not informative only. From this point of view, one of the scientific ways to study the economic data is "Statistical Modeling" through the applicable concept of "Copula Function". In this paper, through the copula functions and the applicable concept of dependence, called "Directional dependence", the dependence structure between variations in family's income and the expenses allocated to buy cultural and miscellaneous goods would be widely studied. Simulation results show that by decreasing the level of income, Iranian families tend to decrease their cultural costs rather than unnecessary miscellaneous costs. 

‎In this paper‎, ‎under certain conditions‎, ‎the usual stochastic‎, ‎convex and dispersive orders between the smallest claim amounts with independent Weibull claims are discussed‎. ‎Also‎, ‎under conditions on some well-known common copula‎, ‎some stochastic comparisons of smallest claim amounts with dependent heterogeneous claims have been obtained‎.

‎The parameters of reliability for the most family marginal distribution is estimated with the assumption of independence between two component stress and strength‎, ‎but‎, ‎unfortunately when these two component are correlated‎, ‎have been less discussed‎. ‎Recently‎, ‎a method based on a copula function for estimating the reliability parameter is proposed under the assumption of correlation between stress and strength components‎. ‎In this paper‎, ‎this method is used to estimate the reliability parameter when the distribution of componets is Generalized Exponential (GE)‎. ‎For this purpose FGM‎, ‎generalized FGM and frank copula function have been used‎. ‎Then simulation is also used to demonstrate the suitability of the estimates‎. ‎In the end‎, ‎reliability parameter for data relative contribution of major groups in terms of age breakdown of the population of urban and rural areas in Iran in the year 1390 will be estimated.

The non-homogeneous bivariate compound Poisson process with short term periodic intensity function is used for modeling the events with seasonal patterns or periodic trends. In this paper, this process is carefully introduced. In order to characterize the dependence structure between jumps, the Levy copula function is provided. For estimating the parameters of the model, the inference for margins method is used. As an application, this model is fitted to an automobile insurance dataset with inference for margins method and its accuracy is compared with the full maximum likelihood method. By using the goodness of fit test, it is confirmed that this model is appropriate for describing the data.

Paying attention to the copula function in order to model the structure of data dependence has become very common in recent decades. Three methods of estimation, moment method, mixture method, and copula moment, are considered to estimate the dependence parameter of copula function in the presence of outlier data. Although the moment method is an old method, sometimes this method leads to inaccurate estimation. Thus, two other moment-based methods are intended to improve that old method. The simulation study results showed that when we use copula moment and mixture moment for estimating the dependence parameter of copula function in the presence of outlier data, the obtained MSEs are smaller. Also, the copula moment method is the best estimate based on MSE. Finally, the obtained numerical results are used in a practical example.

Systemic risk, as one of the challenges of the financial system, has attracted special attention from policymakers, investors, and researchers. Identifying and assessing systemic risk is crucial for enhancing the financial stability of the banking system. In this regard, this article uses the Conditional Value at Risk method to evaluate the systemic risk of simulated data and Iran's banking system. In this method, the conditional mean and conditional variance are modeled using Autoregressive Moving Average and Generalized Autoregressive Conditional Heteroskedasticity models, respectively. The data studied includes the daily stock prices of 17 Iranian banks from April 8, 2019, to May 1, 2023, which contains missing values in some periods. The Kalman filter approach has been used for interpolating the missing values. Additionally, Vine copulas  with a hierarchical tree structure have been employed to describe the nonlinear dependencies and hierarchical risk structure of the returns of the studied banks. The results of these calculations indicate that Bank Tejarat has the highest systemic risk, and the increase in systemic risk, in addition to causing financial crises, has adverse effects on macroeconomic performance. These results can significantly help in predicting and mitigating the effects of financial crises and managing them effectively.