Enjoy the Joy of Copulas: With a Package<b>copula</b>

Yan, Jun

doi:10.18637/jss.v021.i04

Cited by 394 publications

(232 citation statements)

References 42 publications

Supporting

Mentioning

221

Contrasting

Unclassified

Order By: Relevance

“…The authors wish to thank Prof. Zhengjun Zhang (University of Wisconsin, US) for his advice about the quotient correlation test, and Prof. Qiang Zhang (Sun Yat-sen University, China) and three anonymous reviewers for their remarks and criticisms that helped improve the quality of the original manuscript. The analyses were performed in R (R Core Team 2013) by using the contributed packages POT (Ribatet 2006), mvtnorm (Genz and Bretz 2009;Genz et al 2011), and copula (Yan 2007;Kojadinovic and Yan 2010). The authors and maintainers of this software are gratefully acknowledged.…”

mentioning

confidence: 99%

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

The simultaneous occurrence of extreme events, such as simultaneous storms and floods at different locations, has a serious impact on risk assessment and mitigation strategies. The joint occurrence of extreme events can be measured by the so-called upper tail dependence (UTD) coefficient k U . In this study, we reconsider the properties of the most popular k U estimators and show that their strong bias and uncertainty make most of the empirical results reported in the hydrological literature questionable. In order to overcome the limits of k U analysis, we test several alternative tools such as a pool of formal statistical tests devised for recognizing upper tail independence and graphical diagnostics based on binary correlation and binary entropy. The reliability of all the methods is preliminarily checked by Monte Carlo experiments. Statistical tests and graphical diagnostics are therefore applied to three different rainfall data sets that allow us to explore the properties of the spatial dependence structure of rainfall extremes over a wide range of spatio-temporal scales ranging from 30 min and 1 km to 30 days and %3000 km. Results highlight that (1) classical estimators provide non zero tail dependence even for cases where it should be zero; (2) formal tests and binary correlation highlight that the pairwise spatial dependence structure can be weaker than Gaussian, thus excluding UTD calculated in a pairwise manner; (3) the binary entropy computed on triples of locations shows that the pairwise UTD is not enough to explain the spatial dependence structure of extreme rainfall, whose complexity becomes evident only after resorting to higher order correlation measures. The results concerning the bias and uncertainty of k U estimators are fully general and suggest avoiding their use especially for the short time series usually available in hydrology.

show abstract

mentioning

confidence: 99%

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Serinaldi

Bàrdossy

Kilsby

2014

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

show abstract

“…; u n T directly with custom written computer code through various parameter optimization approaches for a range of copula families of which Table 4 is only a small selection of the very extensive range of possible copula families this is no longer strictly essential. This is due to the fact that Yan [36] developed a R based package copula which is now readily available to researchers worldwide, and which has subsequently been expanded by Kojadinovic and Yan [37] for multivariate distribution modelling using copulas. As a result the use of R based open source statistical software from the Comprehensive R Archive Network is now commonly available to researchers worldwide and is accepted as a standard statistical tool within the statistics community.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

Ramnath

2017

Int. J. Metrol. Qual. Eng.

View full text Add to dashboard Cite

Abstract. In the field of pressure metrology the effective area is A e = A 0 (1 + lP) where A 0 is the zero-pressure area and l is the distortion coefficient and the conventional practise is to construct univariate probability density functions (PDFs) for A 0 and l. As a result analytical generalized non-Gaussian bivariate joint PDFs has not featured prominently in pressure metrology. Recently extended lambda distribution based quantile functions have been successfully utilized for summarizing univariate arbitrary PDF distributions of gas pressure balances. Motivated by this development we investigate the feasibility and utility of extending and applying quantile functions to systems which naturally exhibit bivariate PDFs. Our approach is to utilize the GUM Supplement 1 methodology to solve and generate Monte Carlo based multivariate uncertainty data for an oil based pressure balance laboratory standard that is used to generate known high pressures, and which are in turn cross-floated against another pressure balance transfer standard in order to deduce the transfer standard's respective area. We then numerically analyse the uncertainty data by formulating and constructing an approximate bivariate quantile distribution that directly couples A 0 and l in order to compare and contrast its accuracy to an exact GUM Supplement 2 based uncertainty quantification analysis.

show abstract

“…For the bivariate case, the copula models are used to generate 1000 random pairs of dependent variables. A procedure of iterative conditioning is applied, which involves the generation of independent variates of one of the variables and then recursive generation of the second variable, by using a conditional distribution (see Yan 2007). Figure 2 illustrates a schematic explanation of the different steps followed for the synthesis of flood events.…”

Section: Synthesis Of Flood Variables and Eventsmentioning

confidence: 99%

Dam risk assessment based on univariate versus bivariate statistical approaches: a case study for Argentina

Poduje

Belli

Haberlandt

2014

Hydrological Sciences Journal

View full text Add to dashboard Cite

Considering floods as multivariate events allows a better statistical representation of their complexity. In this work the relevance of multivariate analysis of floods for designing or assessing the safety of hydraulic structures is discussed. A flood event is characterized by its peak flow and volume. The dependence between the variables is modelled with a copula. One thousand random pairs of variables are transformed to hydrographs, applying the Beta distribution function. Synthetic floods are routed through a reservoir to assess the risk of overtopping a dam. The resulting maximum water levels are compared to estimations considering the peak flow and volume separately. The analysis is performed using daily flows observed in the River Agrio in Neuquén Province, Argentina, a catchment area of 7300 km 2 . The bivariate approach results in higher maximum water level values. Therefore the multivariate approach should be preferred for the estimation of design variables.

show abstract

Enjoy the Joy of Copulas: With a Packagecopula

Cited by 394 publications

References 42 publications

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Upper tail dependence in rainfall extremes: would we know it if we saw it?

Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties

Dam risk assessment based on univariate versus bivariate statistical approaches: a case study for Argentina

Contact Info

Product

Resources

About