Distribution function of a bivariate copula

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Description

This function evaluates the cumulative distribution function (CDF) of a given parametric bivariate copula.

Usage

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BiCopCDF(u1, u2, family, par, par2=0)

Arguments

u1,u2

Numeric vectors of equal length with values in [0,1].

family

An integer defining the bivariate copula family:
0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
7 = BB1 copula
8 = BB6 copula
9 = BB7 copula
10 = BB8 copula
13 = rotated Clayton copula (180 degrees; “survival Clayton”)
14 = rotated Gumbel copula (180 degrees; “survival Gumbel”)
16 = rotated Joe copula (180 degrees; “survival Joe”)
17 = rotated BB1 copula (180 degrees; “survival BB1”)
18 = rotated BB6 copula (180 degrees; “survival BB6”)
19 = rotated BB7 copula (180 degrees; “survival BB7”)
20 = rotated BB8 copula (180 degrees; “survival BB8”)
23 = rotated Clayton copula (90 degrees)
24 = rotated Gumbel copula (90 degrees)
26 = rotated Joe copula (90 degrees)
27 = rotated BB1 copula (90 degrees)
28 = rotated BB6 copula (90 degrees)
29 = rotated BB7 copula (90 degrees)
30 = rotated BB8 copula (90 degrees)
33 = rotated Clayton copula (270 degrees)
34 = rotated Gumbel copula (270 degrees)
36 = rotated Joe copula (270 degrees)
37 = rotated BB1 copula (270 degrees)
38 = rotated BB6 copula (270 degrees)
39 = rotated BB7 copula (270 degrees)
40 = rotated BB8 copula (270 degrees)

par

Copula parameter.

par2

Second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8; default: par2 = 0).

Value

A numeric vector of the bivariate copula distribution function evaluated at u1 and u2.

Author(s)

Eike Brechmann

See Also

BiCopPDF, BiCopHfunc, BiCopSim

Examples

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# simulate from a bivariate t-copula
simdata = BiCopSim(300,2,-0.7,par2=4)

# evaluate the distribution function of the bivariate t-copula
u1 = simdata[,1]
u2 = simdata[,2]
BiCopCDF(u1,u2,2,-0.7,par2=4)

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