BiCopCondSim: Conditional simulation from a Bivariate Copula

In tnagler/VineCopula: Statistical Inference of Vine Copulas

Conditional simulation from a Bivariate Copula

Description

This function simulates from a parametric bivariate copula, where on of the variables is fixed. I.e., we simulate either from C_{2|1}(u_2|u_1;\theta) or C_{1|2}(u_1|u_2;\theta), which are both conditional distribution functions of one variable given another.

Usage

BiCopCondSim(
  N,
  cond.val,
  cond.var,
  family,
  par,
  par2 = 0,
  obj = NULL,
  check.pars = TRUE
)

Arguments

N	Number of observations simulated.
cond.val	numeric vector of length N containing the values to condition on.
cond.var	either 1 or 2; the variable to condition on.
family	integer; single number or vector of size N; 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 N; copula parameter.
par2	numeric; single number or vector of size N; 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 a 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).

Details

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

BiCopCondSim(N, cond.val, cond.var, obj)

can be used.

Value

A length N vector of simulated from conditional distributions related to bivariate copula with family and parameter(s) par, par2.

Author(s)

Thomas Nagler

See Also

BiCopCDF(), BiCopPDF(), RVineSim()

Examples

# create bivariate t-copula
obj <- BiCop(family = 2, par = -0.7, par2 = 4)

# simulate 500 observations of (U1, U2)
sim <- BiCopSim(500, obj)
hist(sim[, 1])  # data have uniform distribution
hist(sim[, 2])  # data have uniform distribution

# simulate 500 observations of (U2 | U1 = 0.7)
sim1 <- BiCopCondSim(500, cond.val = 0.7, cond.var = 1, obj)
hist(sim1)  # not uniform!

# simulate 500 observations of (U1 | U2 = 0.1)
sim2 <- BiCopCondSim(500, cond.val = 0.1, cond.var = 2, obj)
hist(sim2)  # not uniform!

tnagler/VineCopula documentation built on April 13, 2025, 1:40 p.m.