CDVine (version 1.4)

BiCopPDF: Density of a bivariate copula

Description

This function evaluates the probability density function (PDF) of a given parametric bivariate copula.

Usage

BiCopPDF(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 density evaluated at u1 and u2.

See Also

BiCopCDF, BiCopHfunc, BiCopSim

Examples

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

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