4 research outputs found

    A kaleidoscopic view of multivariate copulas and quasi-copulas

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    Focal copulas: a common framework for various classes of semilinear copulas

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    A new method to construct semi-copulas is introduced. These semi-copulas are called focal semi-copulas and their construction is based on linear interpolation on segments connecting the diagonal of the unit square with two focal points. Several classes of semilinear semi-copulas, such as lower semilinear semi-copulas, upper semilinear semi-copulas, ortholinear semi-copulas and biconic semi-copulas with a given diagonal section, turn out to be special cases of focal semi-copulas. Subclasses of focal semi-copulas, such as focal (quasi-)copulas are characterized as well

    Semilinear and semiquadratic conjunctive aggregation functions

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    Biconic semi-copulas with a given section

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    Inspired by the notion of biconic semi-copulas, we introduce biconic semi-copulas with a given section. Such semi-copulas are constructed by linear interpolation on segments connecting the graph of a continuous and decreasing function to the points (0, 0) and (1, 1). Special classes of biconic semi-copulas with a given section such as biconic (quasi-)copulas with a given section are considered. Some examples are also provided
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