Equicoordinate Quantiles of the Multivariate Normal Distribution

Computes the equicoordinate quantile \(q\) such that \(P(X_1 \le q, X_2 \le q, \ldots, X_k \le q) = p\) for a multivariate normal random vector \(X\).

qmvnormr(
  p,
  mean = NULL,
  sigma,
  n0 = 1024,
  n_max = 16384,
  R = 8,
  abseps = 1e-04,
  releps = 0,
  seed = 314159,
  parallel = TRUE,
  nthreads = 0
)

Arguments

p: The probability level (cumulative probability).
mean: The mean vector. If NULL (default), a zero vector of appropriate length is used.
sigma: The covariance (or correlation) matrix of the distribution.
n0: Initial number of samples per replication for the Monte Carlo integration.
n_max: Maximum number of samples allowed per replication.
R: Number of independent replications used to estimate the error.
abseps: Absolute error tolerance for the probability calculation.
releps: Relative error tolerance for the probability calculation.
seed: Random seed for reproducibility. If 0, a seed is generated from the computer clock.
parallel: Logical; if TRUE, computations are performed in parallel.
nthreads: Number of threads for parallel execution. If 0, the default RcppParallel behavior is used.

Value

A numeric value representing the calculated equicoordinate quantile.

Details

This function finds the value \(q\) using a root-finding algorithm applied to the pmvnormr function. It solves for the value where the multivariate normal cumulative distribution function equals the target probability \(p\).

Positive semidefinite sigma matrices (including singular cases) are supported in the general covariance branch via minimal diagonal stabilization during factorization.

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples


n <- 5
mean <- rep(0, n)
sigma <- matrix(0.5, n, n)
diag(sigma) <- 1
qmvnormr(0.5, mean = mean, sigma = sigma, nthreads = 1)
#> [1] 0.8150347