qmvnormr: Equicoordinate Quantiles of the Multivariate Normal...

In lrstat: Power and Sample Size Calculation for Non-Proportional Hazards and Beyond

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
)

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.

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.

Value

A numeric value representing the calculated equicoordinate quantile.

Author(s)

Kaifeng Lu, [e-mail]

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)

lrstat documentation built on Aug. 25, 2026, 5:07 p.m.