lrstat (version 0.3.3)

qmvnormr: Equicoordinate Quantiles of the Multivariate Normal Distribution

Description

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,
  n0 = 1024,
  n_max = 16384,
  R = 8,
  abseps = 1e-04,
  releps = 0,
  seed = 314159,
  parallel = TRUE,
  nthreads = 0
)

Value

A numeric value representing the calculated equicoordinate quantile.

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.

Author

Kaifeng Lu,

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.

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)