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‎Copula functions as a model can show the relationship between variables‎. ‎Appropriate copula function for a specific application is a function that shows the dependency between data in a best way‎. ‎Goodness of fit tests theoretically are the best way in selection of copula function‎. ‎Different ways of goodness of fit for copula exist‎. ‎In this paper we will examine the goodness of fit tests from theoretical point of view and evaluate three different methods for comparing the copula functions as well as numerical comparison in order to show the advantage and weak points of each method‎. ‎At the end we will analyze the methods of discussed test by using the information from Tehran Stock Exchange‎. 

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‎Maximum likelihood estimation of multivariate distributions needs solving a optimization problem with large dimentions (to the number of unknown parameters) but two‎- ‎stage estimation divides this problem to several simple optimizations‎. ‎It saves significant amount of computational time‎. ‎Two methods are investigated for estimation consistency check‎. ‎We revisit Sankaran and Nair's bivariate Pareto distribution as an example‎. ‎Two data sets (simulated data and real data) have been analyzed for illustrative purposes‎.

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‎One of the most common reasons of corneal transplantation in Iran is Keratoconus‎. ‎Keratoconus is a non-inflammatory phenomenon which usually affects the cornea of both eyes‎. ‎Since in corneal transplantation a portion of people may not reject the transplanted organ so for studying the effective factors on survival time of these data‎ , ‎the survival analysis with cure ratio was used‎.

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‎A copula function is a useful tool in identifying the dependency structure of dependent data and thus fitting a proper distribution to the existing data set. In this paper, using the copula function for stock market data including three variables of financial weakness, accumulated profit, and tangible assets related to 110 Iranian trading companies from 1385 to 1389 is analyzed and especially a three-dimensional distribution of these data is appropriate. We used a variety of tools to examine the dependency type in the data set, containing the scatter, chi, and Kendall plots. We also analyze the directional and tail dependency of the data set and calculated the dependence coefficients of Kendall tau and Spearman rho. Finally, we perform a good fitness of fit test for a few well-known copula functions, so that we can get the right copula function of the data set coming from the stock market.

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Copula functions are  useful tools in modeling the dependence between random variables, but most existing copula functions are symmetric, while in many applications, asymmetric joint functions are required. One of these applications is reliability modeling, where asymmetric joint functions can explain different tail dependencies and provide a better model. Therefore, the theory of constructing asymmetric copula functions that can model a wider range of data has been developed. In this research, while reviewing the methods of creating asymmetric copula functions that can provide various tail dependencies, these functions are used to estimate the two-dimensional reliability of data on the age an usage of Rana and Dana cars.

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Drought is one of the most important concepts in hydrology, which has gained increased significance in recent years,
and the results of its modeling and analysis are crucial for risk assessment and management. This study examines drought at
the Zahedan station during the statistical period from 1951 to 2017 using the standardized precipitation index and explains
multivariate data modeling methods using Vine Copulas. Various models are compared using goodness-of-fit criteria, and
the best model is selected. Additionally, joint return periods are calculated and analyzed.