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A recipe for bivariate copulas

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  • Eric Key

Abstract

We give conditions on a ⩾ −1, b ∈ ( − ∞, ∞), and f and g so that Ca, b(x, y) = xy(1 + af(x)g(y))b is a bivariate copula. Many well-known copulas are of this form, including the Ali–Mikhail–Haq Family, Huang–Kotz Family, Bairamov–Kotz Family, and Bekrizadeh–Parham–Zadkarmi Family. One result is that we produce an algorithm for producing such copulas. Another is a one-parameter family of copulas whose measures of concordance range from 0 to 1.

Suggested Citation

  • Eric Key, 2016. "A recipe for bivariate copulas," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6416-6420, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:21:p:6416-6420
    DOI: 10.1080/03610926.2014.915040
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