×

A recipe for bivariate copulas. (English) Zbl 1349.62240

Summary: We give conditions on \(a\geq -1\), \(b\in (\infty,\infty)\), and \(f\) and \(g\) so that \(C_{a,b}(x,y) = xy(1+af(x)g(y))^b\) 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.

MSC:

62H20 Measures of association (correlation, canonical correlation, etc.)
62F40 Bootstrap, jackknife and other resampling methods
62E10 Characterization and structure theory of statistical distributions

Keywords:

copulas
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/s001840100158 · Zbl 1433.62044 · doi:10.1007/s001840100158
[2] Bekrizadeh H., Appl. Math. Sci. 6 (71) pp 3527– (2012)
[3] DOI: 10.1007/s001840050030 · Zbl 1093.62514 · doi:10.1007/s001840050030
[4] Nelsen R.B., Properties and Applications of Copulas: A Brief Survey (2003)
[5] Scarsini M., Stochastica 8 pp 201– (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.