BACKGROUND AND OBJECTIVES: The estimate of reserved claims is based on the prediction of the final amount of claims that have not yet been settled and which the insurer has undertaken to pay. The micro-level approach estimates the amount of each unsettled claim separately. In this context, the time taken to settle a claim is an important variable, as large claims usually take longer to settle and may not be paid in the relevant financial period. Non-payment of claims may be due to a lack of timely reporting, a high volume of cases or legal complications. Therefore, there may also be censored data. In this article, we use the Copula function approach to model the dependency structure of the settlement duration and claim amount variables.METHODS: In this study, the amount of each unpaid claim is estimated separately using a micro-level approach. For this purpose, the duration of the settlement of each claim is considered as a variable that depends on the amount of the claim. Based on the modeling of the dependency structure between the claim amount and the settlement duration using the Copula function and using the general characteristics of the claims as predictor variables, each unpaid claim is estimated. The marginal distributions of the claim amount and the settlement period based on covariates explain the stochastic behavior of each of them and are modeled separately. In the Copula function approach, the dependence structure of the variables can be considered separately from their marginal distributions. By choosing or constructing an acceptable and appropriate Copula function with the dependence structure of the claim amount and the duration of its settlement, and taking into account the particular characteristics and conditions of inflation, the amount of an unpaid claim can be estimated more accurately. In this study, the accuracy of the estimation and the validity of the proposed model are evaluated using simulations.FINDINGS: The proposed method is implemented for the data collection of one of the insurance companies regarding the cases of the employer's professional liability claims in 8 years, from March 2013 to March 2021, which includes unpaid claims. In order to evaluate the error in estimating the claim amount with this method in this data set, 1000 samples are taken from the data whose claim amount is known and settled and each time a number similar to the actual number is censored, the known values are censored and their amount is estimated. Then the estimation error is calculated using the criteria mentioned in the article. And finally, it can be seen that the results have a good accuracy rate.CONCLUSION: In the article, it can be seen that the selected Copula function has acceptable results for the estimation of reserved claims.

Gardening products, like apple, are exposed to a variety of risks caused by unfavorable weather conditions. This kind of risk is unavoidable, but manageable. Agricultural insurance is an effective scheme in weather risk management. Nevertheless, current insurance schemes have challenges, such as high transaction costs, and problems caused by asymmetric information, i. e. adverse selection and moral hazard. Therefore, this study aimed to present an appropriate insurance scheme for apple production in Damavand, the so-called “ weather-based index insurance” . In this regard, the information on apple yield and weather variables was collected between 1987-2016, from Iranian Agriculture Jihad Organization and the local meteorological station. The dependency structure between apple yield and weather variables was investigated by C-Vine Copula as a joint distribution to compute the expected loss. Then, according to the expected loss, weatherbased index insurance premium was measured. The premium amount was equal to Thousand Rials 32, 546. 11 in the crop year 2016-17, which is different from the current insurance premium. This difference is because of the distinct nature of the two insurance schemes and the imperative and official mode of current insurance scheme.

In this article a spatial model is presented for extreme values with marginal generalized extreme value (GEV) distribution. The spatial model would be able to capture the multi-scale spatial dependencies. The small scale dependencies in this model is modeled by means of Copula function and then in a hierarchical manner a random field is related to location parameters of marginal GEV distributions in order to account for large scale dependencies. Bayesian inference of presented model is accomplished by offered Markov chain Monte Carlo (MCMC) design, which consisted of Gibbs sampler, random walk Metropolis-Hastings and adaptive independence sampler algorithms. In proposed MCMC design the vector of location parameters is updated simultaneously based on devised multivariate proposal distribution. Also, we attain Bayesian spatial prediction by approximation of the predictive distribution. Finally, the estimation of model parameters and possibilities for capturing and separation of multi-scale spatial dependencies are investigated in a simulation example and analysis of wind speed extremes.

Introduction: In recent years, the use of Copula function for modeling multivariate survival data has been drastically increased. One of multivarite survival data is competing risk data.Aim: The purpose of this study is to introduce bayesian analysis of competing risk data using possitive stable Copula function. At the end we used the proposed model on the Diethylstilbestrol clinical trial data. In this clinical trial 506 prostate cancer patients were treated using different dosage of Diethylstilbestrol drug.Materials and Methods: After constructing likelihood function using Copula, by choosing appropriate prior distribution for parameters, we obtain the posterior distribution of parameters using the Metropolis-Hastings algorithms and Slice sampling.Result: Fitting bayesian models to the data indicated that the effect of type of treatment on the time of the death from prostate cancer depended on age and weight of the patiens. The results is in line with the clasic methods.Conclustion: The obtained estimation of Tau Kendall correlation coefficien shows less variation in Bayesian model compared with classical model.

Introduction Spatial and temporal variations of soil characteristics occur in large and small scales. Investigating the variability of soil parameters is considered as one of the requirements for proper management of fertilizer resources in a sustainable agricultural system. Studying of these variation is very time-consuming and costly especially in large scales. In order to the fast and reliable determination of the soil properties, various interpolation techniques have been developed and applied. The most widely used interpolation technique is the different Kriging types. The Copula function is one of the new interpolation techniques that are recently used in sciences such as hydrology. Thus, the aim of this research was to evaluate the spatial variation of some soil chemical properties using the Copula function and comparisons with geostatistics techniques. Materials and Methods Sampling by regular networking was done in an area of 484 ha located in 10 km far from the west of Baft city, located in Kerman province, central Iran (latitude of 29° 15′ N and longitude of 56° 29′ E). In the studied area, three agricultural, pasture and industrial sites are located nearby. The common crops of the region are wheat, barley, alfalfa, legumes and orchards of walnuts, pomegranates, almonds and grapes. The average height of the studied area is 2270 meters above sea level, the average annual temperature of the area is 16 degrees Celsius, and the average annual precipitation of the area is 247 mm. The soil used for the experiment was collected from 0 to 20 cm depth of the field. 121 soil samples were air-dried and, some physical and chemical properties were measured. In order to fit the Copula function to the data, first the appropriate marginal distribution function should be fitted to the data. For this purpose, three tests were used: Kolmogorov-Smirnov, Anderson-Darling and Chi-Square. The mentioned tests were carried out in the EasyFit 5.5 statistical software. By fitting the best marginal distribution function, the cumulative value of the marginal distribution function is calculated for each data. After calculating the above values, detailed functions can be fitted to the data. Finally, the accuracy of each interpolation method was evaluated according to the root mean square Error (RMSE), coefficient of determination (R2), mean absolute error (MAE) and mean biass error (MBE) indices. Results and Discussion In all types of geostatistical methods, the first step in interpolation is to fit the semivaiogram to the measured data, so after normalizing the data and validating the models, the appropriate model was selected for fitting the semivaiogram. Among the measured parameters, Pava and Kava semivaiogram followed spherical model and the interpolation of the above variables was done on the basis of this model. Copula analysis showed that the available phosphorous and potassium variables followed from the Wakeby and gamma distribution function, respectively. Also, based on the Pearson correlation coefficient, the correlation between pairs of points was less than 2000 m and the distance more than 2000 m was known as an independent distance. Based on the validation criteria for Pava parameter, Median Copula function, Average Copula function, IDW, Ordinary Kriging, Disjunctive Kriging, Universal Kriging and Simple Kriging have better estimates, respectively, and in the same way, the best interpolator for Kava parameter Median Copula function, Average Copula function, Ordinary Kriging, Universal Kriging, Disjunctive Kriging, Simple Kriging and IDW were determined, respectively. The estimation performance based on the coefficient of determination (R2) showed that value of this coefficient for Copula function for available phosphorous and potassium were 5% and 4% greater than conventional geostatistics techniques. Also, the error of estimation was less for Copula function indicating the better performance of Copula to estimate the mentioned soil propertiesConclusion This study was performed to investigate the Feasibility study of Copula function in predicting some soil nutrients and comprising this method with widely used methods of geostatistics. Our results demonstrated that the Copula function method is more capable than the classical geostatistical methods in estimating soil properties due to the non-dependence of this method on the normality of the data distribution and outlier data. Therefore, with the help of this method, having a reliable and high-quality data bank of soil characteristics, acceptable maps of other soil characteristics can be presented at various scales.

Copulas are essential probability tools for characterizing the joint distribution of random variables. In this article, we contribute to the topic by studying special bivariate Copulas. They have the property of being defined with piecewise components and are designed for the analysis of data that have dependence structures with distinct substructures in square zones. The theoretical properties of the Copulas are studied, with emphasis on their mathematical validity and some dependence measures. In particular, it is shown that the Kendall tau coefficient has a simple expression that is governed by several parameters, demonstrating the flexibility of the approach. In addition, a real data example is provided to demonstrate the applicability of the Copulas. Fair comparisons with other standard Copulas motivate their use in other practical scenarios.

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.

Background and Objectives: Spatial and temporal variations of soil characteristics occur in large and small scales. Study of these variations is very time-consuming and costly especially in large scales. In order to the fast and reliable determination of soil properties, various interpolation techniques have been developed and applied. The most widely used interpolation techniques in various sciences is the Kriging types. The Copula function is one of the new interpolation techniques that are widely used in sciences such as hydrology. Thus, the aim of this study was to evaluate the spatial variations of some soil physical properties using Copula function and to compare with geostatistics techniques. Materials and Methods: Sampling by regular networking was done in an area of 484 ha located in 10 km from the west of Baft city, Kerman province and finally, 121 surface soil samples were collected. After air drying, the apparent bulk density was determined using the Hunk, then the soil samples were passed through a 2 mm sieve to determine the percentage of sand. To interpolate, four functions of the Archimedean Copula including the Clayton, Frank, Gumbel and Joe functions, and geostatistics techniques including simple, ordinary, universal and disjunctive Kriging and the Inverse Distance Weighting (IDW) method were used. The results were analyzed using Root Mean Square Error (RMSE), determination coefficient (R2), Mean Absolute Error (MAE) and Mean Bias Error (MBE). Results: Based on the descriptive statistics, soil bulk density and soil sand followed a normal and skewed distribution, respectively. In order to fit the Copula function, the distribution functions of the studied variables were firstly determined. The results showed that the sand and bulk density followed the Frechet (3P) and Wakeby distribution functions, respectively. Also, based on the Pearson correlation coefficient, the correlation between pairs of points was determined in distances less than 2000 m and distances more than 2000 m were known as an independent distance. The estimation efficiency based on the determination coefficient (R2) showed that value of determination coefficient for Copula function for the sand variable, 6% and for bulk density 8%, more than conventional geostatistics techniques were obtained. Also, the estimation error of Copula function was minimum that indicate good performance of Copula function to estimate the spatial variation of soil physical properties. Conclusion: The results of study showed that Copula function, especially the median Copula, have the better performance for estimation the studied soil properties. One of the most important reasons for this superiority is the ability to fit the marginal distribution function on the data in Copula, while it is not possible in geostatistics techniques. Other reasons include the ability to express the correlation between the data at different intervals and the lack of sensitivity to outlier data in Copula relative to conventional geostatistics techniques. Due to the skewness nature of soil data, as well as the need for more accurate analysis and interpretation of actual soil data, Copula functions can be widely used to estimate of soil properties.

Drought is an integral part of natural hazards. It usually occurs gradually and without any warning. Moreover, this phenomenon is usually created over time and does not disappear quickly. Recently, some factors such as climate variability and the impact of climate change have influenced drought frequency and intensity in many parts of the world. Various definitions have been provided for drought but in general the lack of water resources in a specific period in a geographical area is considered as drought which implies this phenomenon as a regional hazard. IRAN is located in an arid and semi-arid region in which it experiences drought frequently. There are different types of drought such as meteorological, hydrological, agricultural and socialeconomic. These types are differentiated based on the influential factors which are rainfall, river flows, soil moisture, and social-economic consequences. There are many indices proposed for measuring drought severity; among them Standardized Precipitation Index (SPI), Palmer Drought Severity Index (PDSI) and Surface Water Supply Index (SWSI) could be mentioned. Each of these indices has its own pros and cons and is suitable for a particular type of drought. Therefore, knowing the types of drought can provide a better understanding of shortages and their characteristics. Various factors are utilized for measuring these indices including precipitation, reservoir storage, discharge, temperature and potential evapotranspiration. In this study the three main aforementioned indices were first calculated for Aharchay watershed, located in East Azerbaijan province. Next based on combining these three indices with another two important parameters, groundwater level and solar radiation, a combined drought index is developed and calculated for the studied region. Considering the fact that the aforementioned parameters and indices have different level of importance in combined index, different weights based on the expert opinions (subjective approach) and the level of variation (objective approach) are assigned to the parameters considering how critical each parameter is in the overall drought analysis. This combined index demonstrated various climatic, hydrological and agricultural aspect of the region. In the next step, bivariate analysis of the two variables, intensity and duration, is carried out using Copula. This is done by first checking the dependency between intensity and duration using Pearson, Spearman, and Kendall correlation coefficients. Second, various Copula functions were fitted such as Gaussian, T, Clayton and Gumbel functions. Third, based on the Ordinary Least Square (OLS) and test, the best Copula functions were used. Lastly, based on the chosen Copula the joint probability distributions were obtained. Two cases named “ OR” and “ AND” were defined for joint probability of the two variables and different return period curves were drawn. The results showed that the most severe drought in this watershed occurred in June 2004. Moreover, by assessing correlation coefficient between the considered indices it is shown that analysis of the drought in a region based solely on one index would neglect other imperative aspects in drought determination which necessitates a more integrated indicator. Furthermore, in bivariate analysis, return periods of “ AND” cases were more than “ OR” case. The results of this study could be utilized in preparedness and monitoring drought.