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 \(P(X_1 \le z, \ldots, X_n \le z) = 1 - \alpha\).

Usage

multz(alpha, k, rho, seed = NULL)

Arguments

alpha

Numeric. Significance level (e.g., 0.05 for a 95% confidence level).

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).

seed

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

Value

Numeric. The upper equicoordinate point \(z\) such that the joint probability of all variables being less than or equal to \(z\) is \(1 - \alpha\).

Examples

alpha <- 0.1  # Significance level (10%)
k <- 3        # Number of variables
rho <- 0.5    # Common correlation coefficient
multz(alpha, k, rho)
#> [1] 1.734036