The Joy of Copulas: Bivariate Distributions with Uniform Marginals

Genest, Christian; MacKay, Jock

doi:10.2307/2684602

Cited by 240 publications

(87 citation statements)

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“…, and τ = 1 − θ −1 for elliptical, Frank and Gumbel copulas in Hult and Lindskog (2002), Genest (1987), and Genest and MacKay (1986), respectively. Note that Kendall's τ only accounts for the dependence dominated by the middle of the data, and it is expected to be similar amongst different families of copulas.…”

Section: Application To the German Socio-economic Panelmentioning

confidence: 99%

Coupling Couples With Copulas: Analysis of Assortative Matching on Risk Attitude

Nikoloulopoulos

Moffatt

2018

Economic Inquiry

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We investigate patterns of assortative matching on risk attitude, using self‐reported (ordinal) data on risk attitudes for males and females within married couples, from the German Socio‐Economic Panel over the period 2004–2012. We apply a novel copula‐based bivariate panel ordinal model. Estimation is in two steps: first, a copula‐based Markov model is used to relate the marginal distribution of the response in different time periods, separately for males and females; second, another copula is used to couple the males' and females' conditional (on the past) distributions. We find positive dependence, both in the middle of the distribution, and in the joint tails, and we interpret this as positive assortative matching (PAM). Hence we reject standard assortative matching theories based on risk‐sharing assumptions, and favor models based on alternative assumptions such as the ability of agents to control income risk. We also find evidence of “assimilation”; that is, PAM appearing to increase with years of marriage. (JEL C33, C51, D81)

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Section: Application To the German Socio-economic Panelmentioning

confidence: 99%

Coupling Couples With Copulas: Analysis of Assortative Matching on Risk Attitude

Nikoloulopoulos

Moffatt

2018

Economic Inquiry

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“…The term 'copula' was first employed by Sklar (1959) and then developed and addressed by many researchers (Galambos, 1978;Genest and Mackay, 1986;Schweizer, 1991;Genest and Rivest, 1993;Shih and Louis, 1995;Joe, 1997;Nelson, 2006). Copulas were defined by Nelson (2006) as "functions that join or 'copula' multivariate distribution functions to their one-dimensional marginal distribution functions".…”

Section: Concept Of Copulamentioning

confidence: 99%

Copula‐based flood frequency (COFF) analysis at the confluences of river systems

Wang

Chang

Yeh

2009

Hydrological Processes

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Abstract:Many civil infrastructures are located near the confluence of two streams, where they may be subject to inundation by high flows from either stream or both. These infrastructures, such as highway bridges, are designed to meet specified performance objectives for floods of a specified return period (e.g. the 100 year flood). Because the flooding of structures on one stream can be affected by high flows on the other stream, it is important to know the relationship between the coincident exceedence probabilities on the confluent stream pair in many hydrological engineering practices. Currently, the National Flood Frequency Program (NFF), which was developed by the US Geological Survey (USGS) and based on regional analysis, is probably the most popular model for ungauged site flood estimation and could be employed to estimate flood probabilities at the confluence points. The need for improved infrastructure design at such sites has motivated a renewed interest in the development of more rigorous joint probability distributions of the coincident flows. To accomplish this, a practical procedure is needed to determine the crucial bivariate distributions of design flows at stream confluences. In the past, the copula method provided a way to construct multivariate distribution functions. This paper aims to develop the Copula-based Flood Frequency (COFF) method at the confluence points with any type of marginal distributions via the use of Archimedean copulas and dependent parameters. The practical implementation was assessed and tested against the standard NFF approach by a case study in Iowa's Des Moines River. Monte Carlo simulations proved the success of the generalized copula-based joint distribution algorithm.

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“…Of particular importance in this article is the class of Archimedean copulas that is based on the mathematical theory of associativity. This class encompasses many families of copulas, a number of which can be of use in statistical modelling; an early reference is Genest and MacKay (1986). A further class of copulas based on iteratively mixing conditional distributions was proposed by Joe (1996).…”

Section: (Iv) Classes Of Copulasmentioning

confidence: 99%

“…where U and V denote standard uniform random variables with joint CDF C. For Archimedean copulas with generator ϕ there is an alternate formula due to Genest and MacKay (1986):…”

Section: (V) Measuring Dependencementioning

confidence: 99%

Using Copulas to Model Switching Regimes with an Application to Child Labour*

Smith

2005

Economic Record

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The copula approach to econometric modelling involves the specification of the separate components of the joint distribution of the random variables of interest: models built for each margin are bound together using a copula function. In this paper, the copula approach is used to construct models for switching regimes. The construct is illustrated by fitting a wage earnings model for child workers in the early 1900s, with regimes governed according to literacy. The results improve on earlier modelling efforts by Poirier and Tobias (2003), finding that a child worker may on average expect a reduction in earnings from being literate.

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The Joy of Copulas: Bivariate Distributions with Uniform Marginals

Cited by 240 publications

References 0 publications

Coupling Couples With Copulas: Analysis of Assortative Matching on Risk Attitude

Coupling Couples With Copulas: Analysis of Assortative Matching on Risk Attitude

Copula‐based flood frequency (COFF) analysis at the confluences of river systems

Using Copulas to Model Switching Regimes with an Application to Child Labour*

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