Calculate the Upper Equicoordinate Point of a Multivariate Normal Distribution

Computes the upper equicoordinate quantile for a multivariate standard normal distribution with unit variances and a common correlation coefficient rho. That is, it returns the value \(z\) such that the joint probability \(P(X_1 \le z, \ldots, X_n \le z) = p\).

Usage

multz(p, k, rho, lower.tail = TRUE, seed = NULL)

Arguments

p

Numeric. Cumulative probability (e.g., 0.95 for the 95th

k

Integer. Number of variables in the multivariate normal distribution. Must be >= 1.

rho

Numeric. Common correlation coefficient between variables (typically between 0 and 1).

lower.tail

Logical. If TRUE (default), probability is \(P(X \le z)\); if FALSE, \(P(X > z)\)

seed

Optional. An object specifying if and how the random number generator should be initialized. Passed to qmvnorm.

Value

Numeric. The equicoordinate quantile \(z\)

Examples

p <- 0.9    # Significance level (10%)
k <- 3      # Number of variables
rho <- 0.5  # Common correlation coefficient
multz(p, k, rho)
#> [1] 1.734036