scholarly journals Modelling the statistical dependence of rainfall event variables by a trivariate copula function

2011 ◽  
Vol 8 (1) ◽  
pp. 429-481 ◽  
Author(s):  
M. Balistrocchi ◽  
B. Bacchi
Keyword(s):  
Goodness Of Fit ◽  
Random Variables ◽  
Joint Probability ◽  
Copula Function ◽  
Rainfall Event ◽  
Probabilistic Methods ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Distribution Fitting ◽  
Independent Events

Abstract. In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by splitting the problem in two distinct items. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein a trivariate probability distribution of the rainfall event volume, the wet weather duration and the interevent time is proposed and verified by test statistics with regard to three long time series recorded in different Italian climates. The function was developed by applying a mixing technique to bivariate copulas, which were formerly obtained by analyzing the random variables in pairs. A unique probabilistic model seems to be suitable for representing the dependence structure, despite the sensitivity shown by the dependence parameters towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.

scholarly journals Modelling the statistical dependence of rainfall event variables through copula functions

2011 ◽  
Vol 15 (6) ◽  
pp. 1959-1977 ◽  
Author(s):  
M. Balistrocchi ◽  
B. Bacchi
Keyword(s):  
Goodness Of Fit ◽  
Joint Probability ◽  
Weibull Model ◽  
Rainfall Event ◽  
Probabilistic Methods ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Copula Functions ◽  
Distribution Fitting ◽  
Independent Events

Abstract. In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by dividing the problem in two distinct parts. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein the dependence structure of the rainfall event volume, the wet weather duration and the interevent time is assessed and verified by test statistics with respect to three long time series recorded in different Italian climates. Paired analyses revealed a non negligible dependence between volume and duration, while the interevent period proved to be substantially independent of the other variables. A unique copula model seems to be suitable for representing this dependence structure, despite the sensitivity demonstrated by its parameter towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.

scholarly journals Measuring compound flood potential from river discharge and storm surge extremes at the global scale

2020 ◽  
Vol 20 (2) ◽  
pp. 489-504 ◽  
Author(s):  
Anaïs Couasnon ◽  
Dirk Eilander ◽  
Sanne Muis ◽  
Ted I. E. Veldkamp ◽  
Ivan D. Haigh ◽  
...  
Keyword(s):  
Storm Surge ◽  
River Discharge ◽  
Flood Hazard ◽  
Joint Probability ◽  
Global Scale ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Meteorological Forcing ◽  
Continental Scale ◽  
Bivariate Dependence

Abstract. The interaction between physical drivers from oceanographic, hydrological, and meteorological processes in coastal areas can result in compound flooding. Compound flood events, like Cyclone Idai and Hurricane Harvey, have revealed the devastating consequences of the co-occurrence of coastal and river floods. A number of studies have recently investigated the likelihood of compound flooding at the continental scale based on simulated variables of flood drivers, such as storm surge, precipitation, and river discharges. At the global scale, this has only been performed based on observations, thereby excluding a large extent of the global coastline. The purpose of this study is to fill this gap and identify regions with a high compound flooding potential from river discharge and storm surge extremes in river mouths globally. To do so, we use daily time series of river discharge and storm surge from state-of-the-art global models driven with consistent meteorological forcing from reanalysis datasets. We measure the compound flood potential by analysing both variables with respect to their timing, joint statistical dependence, and joint return period. Our analysis indicates many regions that deviate from statistical independence and could not be identified in previous global studies based on observations alone, such as Madagascar, northern Morocco, Vietnam, and Taiwan. We report possible causal mechanisms for the observed spatial patterns based on existing literature. Finally, we provide preliminary insights on the implications of the bivariate dependence behaviour on the flood hazard characterisation using Madagascar as a case study. Our global and local analyses show that the dependence structure between flood drivers can be complex and can significantly impact the joint probability of discharge and storm surge extremes. These emphasise the need to refine global flood risk assessments and emergency planning to account for these potential interactions.

scholarly journals Measuring compound flood potential from river discharge and storm surge extremes at the global scale and its implications for flood hazard

2019 ◽  
Author(s):  
Anaïs Couasnon ◽  
Dirk Eilander ◽  
Sanne Muis ◽  
Ted I. E. Veldkamp ◽  
Ivan D. Haigh ◽  
...  
Keyword(s):  
Storm Surge ◽  
River Discharge ◽  
Flood Hazard ◽  
Joint Probability ◽  
Global Scale ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Meteorological Forcing ◽  
Continental Scale ◽  
Bivariate Dependence

Abstract. The interaction between physical drivers from oceanographic, hydrological, and meteorological processes in coastal areas can result in compound flooding. Compound flood events, like Cyclone Idai and Hurricane Harvey, have revealed the devastating consequences of the co-occurrence of coastal and river floods. A number of studies have recently investigated the likelihood of compound flooding at the continental scale based on simulated variables of flood drivers such as storm surge, precipitation, and river discharges. At the global scale, this has only been performed based on observations, thereby excluding a large extent of the global coastline. The purpose of this study is to fill this gap and identify potential hotspots of compound flooding from river discharge and storm surge extremes in river mouths globally. To do so, we use daily time-series of river discharge and storm surge from state-of-the-art global models driven with consistent meteorological forcing from reanalysis datasets. We measure the compound flood potential by analysing both variables with respect to their timing, joint statistical dependence, and joint return period. We find many hotspot regions of compound flooding that could not be identified in previous global studies based on observations alone, such as: Madagascar, Northern Morocco, Vietnam, and Taiwan. We report possible causal mechanisms for the observed spatial patterns based on existing literature. Finally, we provide preliminary insights on the implications of the bivariate dependence behaviour on the flood hazard characterisation using Madagascar as a case study. Our global and local analyses show that the dependence structure between flood drivers can be complex and can significantly impact the joint probability of discharge and storm surge extremes. These emphasise the need to refine global flood risk assessments and emergency planning to account for these potential interactions.

scholarly journals Compound Archimedean Copulas

2021 ◽  
Vol 10 (3) ◽  
pp. 126
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Copula Function ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Unique Structure ◽  
The Family ◽  
The Many

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.

scholarly journals Dependence Modeling in Energy Markets using Sibuya-type Copulas

2017 ◽  
Vol 6 (3) ◽  
pp. 43
Author(s):  
Nikolai Kolev ◽  
Jayme Pinto
Keyword(s):  
Goodness Of Fit ◽  
Basic Assumption ◽  
Energy Markets ◽  
Dependence Structure ◽  
Dependence Function ◽  
Dependence Modeling ◽  
Goodness Of Fit Tests ◽  
Oil And Natural Gas ◽  
Error Terms ◽  
Time Invariant

The dependence structure between 756 prices for futures on crude oil and natural gas traded on NYMEX is analyzed  using  a combination of novel time-series and copula tools.  We model the log-returns on each commodity individually by Generalized Autoregressive Score models and account for dependence between them by fitting various copulas to corresponding  error terms. Our basic assumption is that the dependence structure may vary over time, but the ratio between the joint distribution of error terms and the product of marginal distributions (e.g., Sibuya's dependence function) remains the same, being time-invariant.  By performing conventional goodness-of-fit tests, we select the best copula, being member of the currently  introduced class of  Sibuya-type copulas.

scholarly journals Joint Modeling of Precipitation and Temperature Using Copula Theory for Current and Future Prediction under Climate Change Scenarios in Arid Lands (Case Study, Kerman Province, Iran)

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
T. Mesbahzadeh ◽  
M. M. Miglietta ◽  
M. Mirakbari ◽  
F. Soleimani Sardoo ◽  
M. Abdolhoseini
Keyword(s):  
Climate Change ◽  
Goodness Of Fit ◽  
Joint Modeling ◽  
Copula Function ◽  
Gaussian Copula ◽  
Climate Change Scenarios ◽  
Climatic Parameters ◽  
Goodness Of Fit Test ◽  
Copula Theory ◽  
Precipitation And Temperature

Precipitation and temperature are very important climatic parameters as their changes may affect life conditions. Therefore, predicting temporal trends of precipitation and temperature is very useful for societal and urban planning. In this research, in order to study the future trends in precipitation and temperature, we have applied scenarios of the fifth assessment report of IPCC. The results suggest that both parameters will be increasing in the studied area (Iran) in future. Since there is interdependence between these two climatic parameters, the independent analysis of the two fields will generate errors in the interpretation of model simulations. Therefore, in this study, copula theory was used for joint modeling of precipitation and temperature under climate change scenarios. By the joint distribution, we can find the structure of interdependence of precipitation and temperature in current and future under climate change conditions, which can assist in the risk assessment of extreme hydrological and meteorological events. Based on the results of goodness of fit test, the Frank copula function was selected for modeling of recorded and constructed data under RCP2.6 scenario and the Gaussian copula function was used for joint modeling of the constructed data under the RCP4.5 and RCP8.5 scenarios.

Statistical Dependence of Input Variables in Doproc Method / Statistická Závislost Vstupních Veličin V Metodě Popv

2012 ◽  
Vol 12 (2) ◽  
pp. 48-58 ◽  
Author(s):  
Petr Janas ◽  
Krejsa Martin
Keyword(s):  
Reliability Assessment ◽  
Random Variables ◽  
Statistical Dependence ◽  
Software System ◽  
Dependent Variables ◽  
Computational Procedures ◽  
Input Variables

Abstract In probabilistic tasks, input random variables are often statistically dependent. This fact should be considered in correct computational procedures. In case of the newly developed Direct Optimized Probabilistic Calculation (DOProC), the statistically dependent variables can be expressed by the socalled multidimensional histograms, which can be used e.g. for probabilistic calculations and reliability assessment in the software system ProbCalc.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

scholarly journals Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Nonlinear Diffusion ◽  
Goodness Of Fit ◽  
Real Data ◽  
Degradation Process ◽  
Copula Function ◽  
Assessment Method ◽  
Unknown Parameters ◽  
Degradation Data ◽  
Proposed Model ◽  
Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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