VineCopula (version 2.3.0)

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'') \cr `14` = rotated Gumbel copula (180 degrees; survival Gumbel'') 16 = rotated Joe copula (180 degrees; survival Joe'') \cr `17` = rotated BB1 copula (180 degrees; survival BB1'') 18 = rotated BB6 copula (180 degrees; survival BB6'')\cr `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)

# }