We define a two-dimensional copula on the unit square. Basic characteristics and theorems concerning copulas are given. The concept of random variables is introduced into the definition and characteristics of copulas. The asymmetry of a pair of random variables is defined using the corresponding copula, provided by Sklar's theroem. The upper limit of asymmetry of general copulas is given. Also calculated is the upper limit of asymmetry of the following classes of copulas: positive and negative quadrant dependent copulas, vertically and horizontally semilinear copulas and finally stohastically decreasing copulas.
|
