pmvss_mc function

Monte Carlo Multivariate Subgaussian Stable Distribution

Computes probabilities of the multivariate subgaussian stable distribution for arbitrary limits, alpha, shape matrices, and location vectors via Monte Carlo (thus the suffix _mc).

pmvss_mc(
  lower = rep(-Inf, d),
  upper = rep(Inf, d),
  alpha = 1,
  Q = NULL,
  delta = rep(0, d),
  which.stable = c("libstable4u", "stabledist")[1],
  n = NULL
)

Arguments

• lower: the vector of lower limits of length n.
• upper: the vector of upper limits of length n.
• alpha: default to 1 (Cauchy). Must be 0<alpha<2
• Q: Shape matrix. See Nolan (2013).
• delta: location vector.
• which.stable: defaults to "libstable4u", other option is "stabledist". Indicates which package should provide the univariate stable distribution in this production distribution form of a univariate stable and multivariate normal.
• n: number of random vectors to be drawn for Monte Carlo calculation.

Returns

a number between 0 and 1, the estimated probability via Monte Carlo

Examples

## print("mvpd (d=2, alpha=1.71):")
U <- c(1,1)
L <- -U
Q <- matrix(c(10,7.5,7.5,10),2)
mvpd::pmvss_mc(L, U, alpha=1.71, Q=Q, n=1e3)
mvpd::pmvss   (L, U, alpha=1.71, Q=Q)

## more accuracy = longer runtime
mvpd::pmvss_mc(L, U, alpha=1.71, Q=Q, n=1e4)

U <- c(1,1,1)
L <- -U
Q <- matrix(c(10,7.5,7.5,7.5,10,7.5,7.5,7.5,10),3)
## print("mvpd: (d=3, alpha=1.71):")
mvpd::pmvss_mc(L, U, alpha=1.71, Q=Q, n=1e3)

References

Nolan JP (2013), Multivariate elliptically contoured stable distributions: theory and estimation. Comput Stat (2013) 28:2067–2089 DOI 10.1007/s00180-013-0396-7