EllDistrSimCond {ElliptCopulas}

Simulation of elliptically symmetric random vectors conditionally to some observed part.

Description

Simulation of elliptically symmetric random vectors conditionally to some observed part.

Usage

EllDistrSimCond(
  n,
  xobs,
  d,
  Sigma = diag(d),
  mu = 0,
  density_R2_,
  genR = list(method = "pinv")
)

Arguments

n

number of observations to be simulated from the conditional distribution.

xobs

observed value of X that we condition on. NA represent unknown components of the vectors to be simulated.

d

dimension of the random vector

Sigma

(unconditional) covariance matrix

mu

(unconditional) mean

density_R2_

(unconditional) density of the squared radius.

genR

additional arguments for the generation of the squared radius. It must be a list with a component method:

• If genR$method == "pinv", the radius is generated using the function Runuran::pinv.new().

• If genR$method == "MH", the generation is done using the Metropolis-Hasting algorithm, with a N(0,1) move at each step.

Value

a matrix of size (n,d) of simulated observations.

References

Cambanis, S., Huang, S., & Simons, G. (1981). On the Theory of Elliptically Contoured Distributions, Journal of Multivariate Analysis. (Corollary 5, p.376)

See Also

EllDistrSim for the (unconditional) simulation of elliptically distributed random vectors.

Examples

d = 3
Sigma = rbind(c(1, 0.8, 0.9),
              c(0.8, 1, 0.7),
              c(0.9, 0.7, 1))
mu = c(0, 0, 0)
result = EllDistrSimCond(n = 100, xobs = c(NA, 2, NA), d = d,
  Sigma = Sigma, mu = mu, density_R2_ = function(x){stats::dchisq(x=x,df=3)})
plot(result)

result2 = EllDistrSimCond(n = 1000, xobs = c(1.3, 2, NA), d = d,
  Sigma = Sigma, mu = mu, density_R2_ = function(x){stats::dchisq(x=x,df=3)})
hist(result2)