My introduction to copulas

An interview with Roger Nelsen

Fabrizio Durante 1 , Giovanni Puccetti 2 , Matthias Scherer 3 ,  and Steven Vanduffel 4
  • 1 Dipartimento di Scienze dell’Economia, Università del Salento, , Lecce, Italy
  • 2 Dipartimento di Economia, Management e Metodi Quantitativi, Università di , Milano, Italy
  • 3 Lehrstuhl für Finanzmathematik, Technische Universität , München, Germany
  • 4 Faculteit Economische en Sociale Wetenschappen, Vrije Universiteit Brussel, , Brussel, Belgium

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  • [2] Alsina, C., R. B. Nelsen, and B. Schweizer (1993). On the characterization of a class of binary operations on distribution functions. Statist. Probab. Lett. 17(2), 85-89.

  • [3] Beneš, V. and J. Štepán (Eds.) (1997). Distributions with Given Marginals and Moment problems. Kluwer Acad. Publ., Dordrecht.

  • [4] Clemen, R. and T. Reilly (1999). Correlations and copulas for decision and risk analysis. Management Sci. 45(2), 208-224.

  • [5] Cuadras, C. M., J. Fortiana, and J. A. Rodriguez-Lallena (Eds.) (2002). Distributions with Given Marginals and Statistical Modelling. Kluwer Acad. Publ., Dordrecht.

  • [6] Dall’Aglio, G. (1959). Sulla compatibilità delle funzioni di ripartizione doppia. Rend. Mat. e Appl. (5) 18, 385-413.

  • [7] Dall’Aglio, G., S. Kotz, and G. Salinetti (Eds.) (1991). Probability Distributions with Given Marginals. Kluwer Acad. Publ., Dordrecht.

  • [8] Deheuvels, P. (1978). Caractérisation complète des lois extrêmes multivariées et de la convergence des types extrêmes. Publ. Inst. Stat. Univ. Paris 23, 1-36.

  • [9] Durante, F., G. Puccetti, and M. Scherer (2015). A journey from statistics and probability to risk theory. Depend. Model. 3(1), 182-195.

  • [10] Durante, F., G. Puccetti, M. Scherer, and S. Vanduffel (2016). Stat Trek. Depend. Model. 4(1), 109-122.

  • [11] Durante, F., G. Puccetti, M. Scherer, and S. Vanduffel (2016). Distributions with given marginals: the beginnings. Depend. Model. 4(1), 237-250.

  • [12] Féron, R. (1956). Sur les tableaux de corrélation dont les marges sont données, cas de l’espace à trois dimensions. Publ. Inst. Statist. Univ. Paris 5, 3-12.

  • [13] Fisher, N. I. and P. K. Sen (Eds.) (1994). The Collected Works of Wassily Hoeffding. Springer, New York.

  • [14] Frank, M. J., R. B. Nelsen, and B. Schweizer (1987). Best-possible bounds for the distribution of a sum-a problem of Kolmogorov. Probab. Theory Related Fields 74(2), 199-211.

  • [15] Fréchet, M. (1951). Sur les tableaux de corrélation dont les marges sont données. Ann. Univ. Lyon, Sect. A (3) 14, 53-77.

  • [16] Fredricks, G. A. and R. B. Nelsen (2007). On the relationship between Spearman’s rho and Kendall’s tau for pairs of continuous random variables. J. Statist. Plan. Infer. 137, 2143-2150.

  • [17] Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics. Wiley, Chichester.

  • [18] Genest, C., J. J. Quesada Molina, J. A. Rodríguez Lallena, and C. Sempi (1999). A characterization of quasi-copulas. J. Multivariate Anal. 69(2), 193-205.

  • [19] Hoeffding, W. (1940). Masstabinvariante Korrelationstheorie. Schriften des Mathematischen Instituts und des Instituts für Angewandte Mathematik der Universität Berlin 5(3), 179-233. English translation as “Scale invariant correlation theory” in [13], pp. 57-107.

  • [20] Hoeffding, W. (1941). Masstabinvariante Korrelationsmasse für diskontinuierliche Verteilungen. Arch. Math. Wirtschafts und Sozialforschung 7, 49-70. English translation as “Scale-invariant correlation for discontinuous disributions” in [13], pp. 109-133.

  • [21] Isaacs, R. (1975). Two mathematical papers without words. Math. Mag. 48, 198.

  • [22] Jouini, M. N. and R. T. Clemen (1996). Copula models for aggregating expert opinions. Oper. Res. 44(3), 444-457.

  • [23] Klement, E. P., R. Mesiar, and E. Pap (2000). Triangular Norms. Kluwer Acad. Publ., Dordrecht.

  • [24] Menger, K. (1942). Statistical metrics. Proc. Nat. Acad. Sci. U.S.A. 8, 535-537.

  • [25] Mikusinski, P., H. Sherwood, and M. D. Taylor (1992). Shuffles of min. Stochastica 13, 61-74.

  • [26] Nelsen, R. B. (1987). Proof without words: The harmonic mean-geometric mean-arithmetic mean-root mean square inequality. Math. Mag. 60, 158.

  • [27] Nelsen, R. B. (1993). Proofs Without Words. Exercises in Visual Thinking. Mathematical Association of America (MAA), Washington DC.

  • [28] Nelsen, R. B. (1999). An Introduction to Copulas. Springer, New York.

  • [29] Nelsen, R. B. (2006). An Introduction to Copulas. Second edition. Springer, New York.

  • [30] Nelsen, R. B., J. J. Quesada Molina, B. Schweizer, and C. Sempi (1996). Derivability of some operations on distribution functions. In L. Rüschendorf, B. Schweizer, and M. D. Taylor (Eds.), Distributions with Fixed Marginals and Related Topics, pp. 233-243. Institute of Mathematical Statistic, Hayward CA.

  • [31] Nelsen, R. B. and M. Úbeda Flores (2005). The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. C. R. Acad. Sci. Paris Sér. I 341(9), 583-586.

  • [32] Netz, R. and W. Noel (2007). The Archimedes Codex: How a Medieval Prayer Book is Revealing the True Genius of Antiquity’s Greatest Scientist. Da Capo Press, Boston MA.

  • [33] Rodríguez Lallena, J. A. (1992). Estudio de la Compatibilidad y Diseño de Nuevas Familias en la Teoría de Cópulas. Aplicaciones. Ph.D. thesis, Universidad de Granada.

  • [34] Schweizer, B. and A. Sklar (1983). Probabilistic Metric Spaces. North-Holland, New York.

  • [35] Schweizer, B. and A. Sklar (2005). Probabilistic Metric Spaces. Dover Publications, Mineola NY.

  • [36] Úbeda Flores, M. (2001). Cópulas y Cuasicópulas: Interrelaciones y Nuevas Propiedades. Aplicaciones. Ph.D. thesis, Universidad de Almería.

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Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.

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