VineCopula (version 2.2.0)

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, obj = NULL,
  check.pars = TRUE)

Arguments

u1, u2

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

family

integer; single number or vector of size length(u1); defines 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) 104 = Tawn type 1 copula 114 = rotated Tawn type 1 copula (180 degrees) 124 = rotated Tawn type 1 copula (90 degrees) 134 = rotated Tawn type 1 copula (270 degrees) 204 = Tawn type 2 copula 214 = rotated Tawn type 2 copula (180 degrees) 224 = rotated Tawn type 2 copula (90 degrees) 234 = rotated Tawn type 2 copula (270 degrees)

par

numeric; single number or vector of size length(u1); copula parameter.

par2

numeric; single number or vector of size length(u1); second parameter for bivariate copulas with two parameters (t, BB1, BB6, BB7, BB8, Tawn type 1 and type 2; default: par2 = 0). par2 should be an positive integer for the Students's t copula family = 2.

obj

BiCop object containing the family and parameter specification.

check.pars

logical; default is TRUE; if FALSE, checks for family/parameter-consistency are omitted (should only be used with care).

Value

A numeric vector of the bivariate copula density

• of the copula family

• with parameter(s) par, par2

• evaluated at u1 and u2.

Details

If the family and parameter specification is stored in a BiCop object obj, the alternative version

BiCopPDF(u1, u2, obj)

can be used.

See Also

BiCopCDF, BiCopHfunc, BiCopSim, BiCop

Examples

# NOT RUN {
## simulate from a bivariate Student-t copula
cop <- BiCop(family = 2, par = -0.7, par2 = 4)
simdata <- BiCopSim(100, cop)

## evaluate the density of the bivariate t-copula
u1 <- simdata[,1]
u2 <- simdata[,2]
BiCopPDF(u1, u2, cop)

## select a bivariate copula for the simulated data
fit <- BiCopSelect(u1, u2)
summary(fit)
## and evaluate its PDF
round(BiCopPDF(u1, u2, fit), 3)

# }