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 \(X\).

Usage

qmvnormr(
  p,
  mean = NULL,
  sigma,
  fast = TRUE,
  n0 = 1024,
  n_max = 16384,
  R = 8,
  abseps = 1e-04,
  releps = 0,
  seed = 0,
  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.
fast: Logical; if TRUE, uses a fast approximation of the univariate normal CDF and quantile functions.
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 \(p\).

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)
#> [1] 0.8150347