Year: 2023
Type: article
Abstract: Two-dimensional distribution function g ( x, y ) defined in [0, 1] 2 is called copula, if g ( x, 1) = x and g (1, y )= y for every x, y . Similarly, s -dimensional copula is a distribution function g ( x 1 , x 2 ,..., x s ) such that every k -dimensional face function g ( 1 , … , 1 , x i 1 , 1 , … , 1 , x i 2 , 1 , … , 1 , x i k , 1 , … , 1 ) g\left( {1, \ldots ,1,{x_{{i_1}}},1, \ldots ,1,{x_{{i_2}}},1, \ldots ,1,{x_{{i_k}}},1, \ldots ,1} \right) is equal to x i 1 x i 2 ... x i k for some but fixed k . In this paper we summarize and extend all known parts of copulas. In this paper we use the following abbreviations: {x} — fractional part of x ; {x} — x mod 1; [x] — integer part of x ; u.d. — uniform distribution ; d.f. — distribution function ; a.d.f. — asymptotic distribution function ; u.d.p. — uniform distribution preserving ; step d.f. — step distribution function ; a.e. — almost everywhere ; #X — cardinality of the set X .
Source: Uniform distribution theory
Authors: Oto Strauch, Vladimír Baláž
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: hybrid
OpenAlex ID: W4385730051