A Primer on Copulas for Count Data

By Christian Genest, Johana Nešlehová. ASTIN Bulletin: The Journal of the International Actuarial Association, 2007

484 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/51939739fbaec61f3e9896712d769830de81bf8a

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Citations in the corpus

On the exact region determined by Kendall's τ and Spearman's ρ (2015, background): “In Genest and Nes̆lehová, (2007), propositions 4 and 5, a slightly different notation (hi,j, αi,j and βi,j instead of up, sp−1 and tπ.”
Copula Theory: An Introduction (2010, background): “nal paper by Marshall [132] and to the in-depth discussion by Genest and Nešlehová [82].”
Multivariate Negative Binomial Models for Insurance Claim Counts (2014, methodology): “Despite of its popularity in dependence modeling, the application of copulas for count data is still in its infancy (Genest and Nešlehová, 2007).”
The Advent of Copulas in Finance (2009, background): “For reviews of these topics, see Genest, Remillard, and Beaudoin (2009) , Genest and Neslehova (2007) and McNeil, Frey, and Embrechts (2005) , respectively.”
A mixed copula model for insurance claims and claim sizes (2012, background): “We like to note that the copula in Sklar's theorem is no longer unique for discrete margins (see also Genest & Neslehova ( 2007 )).”
Pair Copula Constructions for Multivariate Discrete Data (2012, background): “The copula C is unique for continuous Y, but is only unique over the Cartesian product of the ranges of the marginal distribution functions when Y is discrete (for more on this issue, see Genest and Nešlehová 2007).”
Spatial contagion between financial markets: a copula-based approach (2010, background): “Notice that, when X and Y are not continuous, the copula associated with them is uniquely determined on Range(F) × Range(G) (for a detailed discussion about this aspect, see [ 13 ]).”
On the empirical multilinear copula process for count data (2014, background): “As shown by Genest and Nešlehová (Astin Bull.”
On a Multivariate Pareto Distribution (2010, unknown): “Generally speaking, there exist a great variety of methods of constructing multivariate dependent probabilistic structures possessing specific univariate margins of interest, with the copulabased approaches being arguably the most popular in nowadays applied actuarial science and practice (see, e.g.”
Flexible Bivariate INAR(1) Processes Using Copulas (2013, methodology): “In the bivariate case we have that for discrete data, the probability mass function (pmf) is obtained by finite differences of the cdf through its copula representation (Genest and Nešlehová, 2007), namely”
Analysis of directional dependence using asymmetric copula-based regression models (2014, background): “Note that the presence of ties in the data may substantially affect the copula estimation.[35] In order to fully facilitate the good properties of the copula, one needs to deal with the discreteness of the variable and the presence of ties in an appropriate way.”
Regression in a copula model for bivariate count data (2010, background): “If F1, F2 are continuous, then C is unique; otherwise, there are many possible copulas as emphasized by Genest and Nes̆lehová [9], but all of these coincide on the closure of Range(F1) × Range(F2), where Range(F ) denotes the range of F .”
Rectangular Patchwork for Bivariate Copulas and Tail Dependence (2009, methodology): “…∈ h with h x = x. Note that the same procedure can be applied in order to describe the class of all copulas with a given horizontal and vertical section (Durante et al., 2007b) as well as to extend a given sub-copula to a copula in all possible ways (see Carley, 2002; Genest and Nešlehová, 2007).”
Count Time Series: A Methodological Review (2021, background): “This construction avoids joint distribution difficulties (see pages 507 and 508 in Genest and Nešlehová (2007)), but keeps the marginal properties of a Poisson process.”