Search Results (13)

This study proposes a hierarchical Archimedean copula (HAC) framework to model the complex dependence structures in hydrodynamic landslide deformations, with a focus on the Donglinxin (DLX) landslide. Hierarchical Archimedean copulas, compared to elliptical copulas, offer greater flexibility by requiring fewer parameters while maintaining broader applicability. The HAC model, combined with pseudo-maximum likelihood estimation (PMLE), is applied to analyze the interdependencies among the landslide-related variables, such as monthly displacement increments, reservoir water level fluctuations, groundwater variations, and precipitation. A case study of the DLX landslide demonstrates the model’s ability to quantify the critical aspects of landslide deformation, including variable correlations, risk thresholds, conditional probabilities, and return periods. The analysis reveals a strong hierarchical dependence between monthly displacement increments and reservoir water level drops. The model also provides valuable insights into the potential risk factors, helping to optimize landslide monitoring and early-warning systems for more effective disaster mitigation. Full article

Insurance companies need to calculate solvency capital requirements in order to ensure that they can meet their future obligations to policyholders and beneficiaries. The solvency capital requirement is a risk management tool essential for addressing extreme catastrophic events that result in a high number of possibly interdependent claims. This paper studies the problem of aggregating the risks coming from several insurance business lines and analyses the effect of reinsurance on the level of risk. Our starting point is to use a hierarchical risk aggregation method which was initially based on two-dimensional elliptical copulas. We then propose the use of copulas from the Archimedean family and a mixture of different copulas. Our results show that a mixture of copulas can provide a better fit to the data than an individual copula and consequently avoid over- or underestimation of the capital requirement of an insurance company. We also investigate the significance of reinsurance in reducing the insurance company’s business risk and its effect on diversification. The results show that reinsurance does not always reduce the level of risk, but can also reduce the effect of diversification for insurance companies with multiple business lines. Full article

During its service life, a deep-sea floating structure is likely to encounter extreme marine disasters. The combined action of wind and wave loads poses a threat to its structural safety. In this study, elliptical copula, Archimedean copula, and vine copula models are employed to depict the intricate dependence structure between wind and waves in a specific sea area of the Shandong Peninsula. Moreover, hourly significant wave height, spectral peak period, and 10 m average wind speed hindcast data from 2004 to 2023 are utilized to explore the joint distribution of multidimensional parameters and environmental design values. The results indicate the following: (1) There exists a significant correlation between wind speed and wave parameters. Among them, the C-vine copula model represents the optimal trivariate joint distribution, followed by the Gaussian copula, while the Frank copula exhibits the poorest fit. (2) Compared with the high-dimensional symmetric copula models, the vine copula model has distinct advantages in describing the dependence structure among several variables. The wave height and period demonstrate upper tail dependence characteristics and follow the Gumbel copula distribution. The optimal joint distribution of wave height and wind speed is the t copula distribution. (3) The identification of extreme environmental parameters based on the joint probability distribution derived from environmental contour lines is more in line with the actual sea conditions. Compared with the design values of independent variables with target return periods, it can significantly reduce engineering costs. In conclusion, the vine copula model can accurately identify the complex dependency characteristics among marine variables, offering scientific support for the reliability-based design of floating structures. Full article

In this study, we assess COVID-19-related mortality in Minnesota and Wisconsin with the aim of demonstrating both the temporal dynamics and the magnitude of the pandemic’s influence from an actuarial risk standpoint. In the initial segment of this paper, we discuss the methodology successfully applied to describe associations in financial and engineering time series. By applying time series analysis, specifically the autoregressive integrated with moving average methods (ARIMA), to weekly mortality figures at the national or state level, we subsequently delve into a marginal distribution examination of ARIMA residuals, addressing any deviation from the standard normality assumption. Thereafter, copulas are utilized to architect joint distribution models across varied geographical domains. The objective of this research is to offer a robust statistical model that utilizes observed mortality datasets from neighboring states and nations to facilitate precise short-term mortality projections. In the subsequent section, our focus shifts to a detailed scrutiny of the statistical interdependencies manifesting between Minnesota and Wisconsin’s weekly COVID-19 mortality figures, adjusted for the time series structure. Leveraging open-source data made available by the CDC and pertinent U.S. state government entities, we apply the ARIMA methodology with subsequent residual distribution modeling. To establish dependence patterns between the states, pair copulas are employed to articulate the relationships between the ARIMA residuals, drawing from fully parametric models. We explore several classes of copulas, comprising both elliptic and Archimedean families. Emphasis is placed on copula model selection. Student t-copula with the marginals modeled by non-standard t-distribution is suggested for ARIMA residuals of Minnesota and Wisconsin COVID mortality as the model of choice based on information criteria and tail cumulation. The copula approach is suggested for the construction of short-term prediction intervals for COVID-19 mortality based on publicly available data. Full article

Rice is not only central to Thailand’s economy and dietary consumption but also plays a significant role in global food security. Northeast Thailand, in particular, is a principal region for rice cultivation. However, with the mounting concerns of climate change, it becomes paramount to understand the interplay between regional weather patterns and rice yields, aiming to develop effective adaptive agricultural strategies. The current study aimed to fill the research gap by investigating an optimal copula for the spatial dependence of rice production and related meteorological variables in this area. The objective of this study is to understand how rice production in different areas relates to each other in order to improve farming practices and address challenges such as suitable weather. To achieve this goal, we apply three families of copulas—elliptical, Archimedean, and extreme—to analyze crop and meteorological variables across the watershed in the northeastern region of Thailand. With a data foundation extending from 1981 to 2021 from the Regional Office of Agricultural Economics Sector 4, Thailand, this study offers a comprehensive analysis of the spatial dynamics driving rice production across twenty provinces in Northeast Thailand. Using a piecewise linear model, we dissected rice yield trends, revealing distinct slopes in production and yield across various periods. The analysis leaned on elliptical, Archimedean, and extreme copula families, using the maximum likelihood estimation to discern marginal distribution residuals. Through rigorous bootstrap goodness-of-fit tests and cross-validation, the most appropriate copula for each province was identified. Key findings demonstrate pronounced spatial interdependencies in rice yields, with the Frank copula prominently capturing the product relationship between provinces such as Maha Sarakham and Roi-Et. Conversely, the Clayton copula better characterized regions such as Srisaket and Ubon Ratchathani. Moreover, the results underscore the considerable influence of meteorological factors, notably rainfall and temperature, on rice production, especially in regions like Ubon Ratchathani. In distilling these multifaceted relationships, the study charts a pathway for crafting sustainable, localized agricultural strategies. As the world grapples with climate change’s ramifications, the insights from this research stand crucial, offering direction for fostering resilience, adaptation, and optimizing rice productivity across Thailand’s diverse agrarian landscapes. Full article

Warmer temperatures significantly influence crop yields, which are a critical determinant of food supply and human well-being. In this study, a probabilistic approach based on bivariate copula models was used to investigate the dependence (described by joint distribution) between crop yield and growing season temperature (T_GS) in the major producing provinces of China for three staple crops (i.e., rice, wheat, and maize). Based on the outputs of 12 models from the Coupled Model Intercomparison Project Phase 6 (CMIP6) under Shared Socioeconomic Pathway 5–8.5, the probability of yield reduction under 1.5 °C and 2 °C global warming was estimated, which has great implications for agricultural risk management. Results showed that yield response to T_GS varied with crop and region, with the most vulnerable being rice in Sichuan, wheat in Sichuan and Gansu, and maize in Shandong, Liaoning, Jilin, Nei Mongol, Shanxi, and Hebei. Among the selected five copulas, Archimedean/elliptical copulas were more suitable to describe the joint distribution between T_GS and yield in most rice-/maize-producing provinces. The probability of yield reduction was greater in vulnerable provinces than in non-vulnerable provinces, with maize facing a higher risk of warming-driven yield loss than rice and wheat. Compared to the 1.5 °C global warming, an additional 0.5 °C warming would increase the yield loss risk in vulnerable provinces by 2–17%, 1–16%, and 3–17% for rice, wheat, and maize, respectively. The copula-based model proved to be an effective tool to provide probabilistic estimates of yield reduction due to warming and can be applied to other crops and regions. The results of this study demonstrated the importance of keeping global warming within 1.5 °C to mitigate the yield loss risk and optimize agricultural decision-making in vulnerable regions. Full article

The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this copula construction are discussed and a further extension outlined. Full article

This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy. Full article

The objective of this study is to compare univariate and joint bivariate return periods of extreme precipitation that all rely on different probability concepts in selected meteorological stations in Cyprus. Pairs of maximum rainfall depths with corresponding durations are estimated and compared using annual maximum series (AMS) for the complete period of the analysis and 30-year subsets for selected data periods. Marginal distributions of extreme precipitation are examined and used for the estimation of typical design periods. The dependence between extreme rainfall and duration is then assessed by an exploratory data analysis using K-plots and Chi-plots and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical, and Extreme Value families are fitted using a pseudo-likelihood estimation method, evaluated according to the corrected Akaike Information Criterion and verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic. The selected copula functions and the corresponding conditional and joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results highlight the effect of sample size on univariate and bivariate rainfall frequency analysis for hydraulic engineering design practices. Full article

Flood frequency estimation for the design of hydraulic structures is usually performed as a univariate analysis of flood event magnitudes. However, recent studies show that for accurate return period estimation of the flood events, the dependence and the correlation pattern among flood attribute characteristics, such as peak discharge, volume and duration should be taken into account in a multivariate framework. The primary goal of this study is to compare univariate and joint bivariate return periods of floods that all rely on different probability concepts in Yermasoyia watershed, Cyprus. Pairs of peak discharge with corresponding flood volumes are estimated and compared using annual maximum series (AMS) and peaks over threshold (POT) approaches. The Lyne-Hollick recursive digital filter is applied to separate baseflow from quick flow and to subsequently estimate flood volumes from the quick flow timeseries. Marginal distributions of flood peaks and volumes are examined and used for the estimation of typical design periods. The dependence between peak discharges and volumes is then assessed by an exploratory data analysis using K-plots and Chi-plots, and the consistency of their relationship is quantified by Kendall’s correlation coefficient. Copulas from Archimedean, Elliptical and Extreme Value families are fitted using a pseudo-likelihood estimation method, verified using both graphical approaches and a goodness-of-fit test based on the Cramér-von Mises statistic and evaluated according to the corrected Akaike Information Criterion. The selected copula functions and the corresponding joint return periods are calculated and the results are compared with the marginal univariate estimations of each variable. Results indicate the importance of the bivariate analysis in the estimation of design return period of the hydraulic structures. Full article

In this study, commonly used copula functions belonging to Archimedean and Elliptical families are fitted to the univariate cumulative distribution functions (CDF) of the drought characteristics duration ( $\text{LD}$ ), average severity ( $\overline{\mathrm{S}}$ ), and average areal extent ( $\overline{\mathrm{A}}$ ) of droughts obtained using standardized precipitation index (SPI) between 1960 and 2013 over Ankara, Turkey. Probabilistic modeling of drought characteristics with seven different fitted copula functions and their comparisons with independently estimated empirical joint distributions show normal copula links drought characteristics better than other copula functions. On average, droughts occur with an average $\text{LD}$ of 6.9 months, $\overline{\mathrm{S}}$ of 0.94, and $\overline{\mathrm{A}}$ of 73%, while such a drought event happens on average once in every 6.65 years. Results also show a very strong and statistically significant relation between $\overline{\mathrm{S}}$ and $\overline{\mathrm{A}}$ , and drought return periods are more sensitive to the unconditioned drought characteristic, while return periods decrease by adding additional variables to the analysis (i.e., trivariate drought analysis compared to bivariate). Full article

In this paper, we demonstrate the superiority of vine copulas over conventional copulas when modeling the dependence structure of a credit portfolio. We show statistical and economic implications of replacing conventional copulas by vine copulas for a subportfolio of the Euro Stoxx 50 and the S&P 500 companies, respectively. Our study includes D-vines and R-vines where the bivariate building blocks are chosen from the Gaussian, the t and the Clayton family. Our findings are (i) the conventional Gauss copula is deficient in modeling the dependence structure of a credit portfolio and economic capital is seriously underestimated; (ii) D-vine structures offer a better statistical fit to the data than classical copulas, but underestimate economic capital compared to R-vines; (iii) when mixing different copula families in an R-vine structure, the best statistical fit to the data can be achieved which corresponds to the most reliable estimate for economic capital. Full article

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in particular on credibility models, dependence structure of claim sizes in collective risk models, and extreme value models for the joint dependence of large losses. We show that specifying certain actuarial models using random shifting or scaling has some advantages for both theoretical treatments and practical applications. Full article