Tarad Jwaid

Conic aggregation functions

Inspired by the notion of conic t-norms, we introduce conic aggregation functions. Such aggregation functions are completely characterized by their zero-set. Special classes of binary conic aggregation functions such as conic quasi-copulas and conic copulas are considered. We provide the necessary and sufficient conditions on the boundary curve of the zero-set of a conic aggregation function to obtain a conic (quasi-) copula and conclude that the class of conic copulas is a proper subclass of the class of conic quasi-copulas. Moreover, we characterize the class of singular conic copulas. We investigate some aggregations of conic (quasi-) copulas. Some examples are also provided.

On a Class of Variolinear Copulas

We construct variolinear copulas with a given diagonal section, i.e. copulas that are linear on line segments connecting points on the diagonal to points on the boundary of the unit square. These line segments cover the unit square, two line segments can only intersect at (0,1) or (1,0), and the line segments may have a varying angle w.r.t. the main diagonal. The class of variolinear copulas covers the subclasses of semilinear, ortholinear and biconic copulas, whose construction has been reported before. We restrict the analysis to the case of symmetric variolinear copulas and we focus on the situation where the variability of the line segments is governed by two linear functions. For that subclass we provide the necessary and sufficient conditions on a diagonal function to obtain a variolinear copula. Some examples are provided.

On the Construction of Semiquadratic Copulas

We introduce several classes of semiquadratic copulas (i.e. copulas that are quadratic in at least one coordinate of any point of the unit square) of which the diagonal section or the opposite diagonal section are given functions. These copulas are constructed by quadratic interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square to the boundaries of the unit square.We provide for each class the necessary and sufficient conditions on a diagonal (resp. opposite diagonal) function and two auxiliary real functions f and g to obtain a copula which has this diagonal (resp. opposite diagonal) function as diagonal (resp. opposite diagonal) section.

Biconic semi-copulas with a given section

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.

Biconic aggregation functions with a given diagonal or opposite diagonal section

A new method to construct aggregation functions is introduced. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction method is based on linear interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square and the points (0, 1) and (1, 0) (resp. (0, 0) and (1, 1)). Special classes of biconic aggregation functions such as biconic semicopulas, quasi-copulas and copulas are studied in detail.