Copulas

Abstract Two-dimensional distribution function g ( x, y ) defined in [0, 1] 2 is called copula, if 1) = x and (1, )= for every . Similarly, s -dimensional copula a 1 , ,..., such that k face g ( 1 , … x i 2 k ) g\left( {1, \ldots ,1,{x_{{i_1}}},1, ,1,{x_{{i_2}}},1, ,1,{x_{{i_k}}},1, ,1} \right) equal to i ... some but fixed In this paper we summarize extend all known parts of copulas. use the following abbreviations: {x} — fractional part ; mod 1; [x] integer u.d. uniform d.f. a.d.f. asymptotic u.d.p. preserving step a.e. almost everywhere #X cardinality set X