Conditional simulation from a Bivariate Copula

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.

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).

Value

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

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.

Author

Thomas Nagler

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!