Abstract
Abstract In this paper we present some of the salient properties of the Bertino family of copulas. We describe the support set of a Bertino copula and show that every Bertino copula is singular. We characterize Bertino copulas in terms of the joint distribution of max (U,V) and min(U,V) when U and V are uniform [0,1] random variables whose copula is a Bertino copula. Finally, we find necessary and sufficient conditions for a Bertino copula to be extremal.
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References
Bertino, S. (1977), Sulla dissomiglianza tra mutabili cicliche. Metron 35, 53–88.
Fredricks, G. A. and R. B. Nelsen (1997), Copulas constructed from diagonal sections. In: V. Beneŝ and J. Ŝtêpán (eds.): Distributions with Given Marginals and Moment Problems, Dordrecht: Kluwer Academic Publishers, pp. 129–136.
Nelsen, R. B. (1999), An Introduction to Copulas. New York: Springer-Verlag.
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Fredricks, G.A., Nelsen, R.B. (2002). The Bertino Family of Copulas. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_10
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DOI: https://doi.org/10.1007/978-94-017-0061-0_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6136-2
Online ISBN: 978-94-017-0061-0
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