Sum_of_Wishart_df {fPASS}

The approximate degrees of freedom formula for sum of Wishart.

Description

The approximate degrees of freedom formula for sum of two independent Wishart random variable with parameter sig1 and sig2, and degrees of freedom n1-1 and n2-1 where n1 + n2 is equal to the total_sample_size.

See Koner and Luo (2023) for more details on the formula for degrees of freedom.

Usage

Sum_of_Wishart_df(total_sample_size, alloc.ratio, sig1, sig2)

Arguments

total_sample_size

Target sample size, must be a positive integer.

alloc.ratio

Allocation of total sample size into the two groups. Must set as a vector of two positive numbers. For equal allocation it should be put as c(1,1), for non-equal allocation one can put c(2,1) or c(3,1) etc.

sig1

The true (or estimate) of covariance matrix for the first group. Must be symmetric (is.symmetric(sig1) == TRUE) and positive definite (chol(sig1) without an error!).

sig2

The true (or estimate) of covariance matrix for the second group. Must be symmetric (is.symmetric(sig2) == TRUE) and positive definite (chol(sig2) without an error!).

Value

The approximate degrees of freedom.

Author(s)

Salil Koner
Maintainer: Salil Koner [e-mail]

See Also

Sim_HotellingT_unequal_var() and pHotellingT().

Examples

k <- 8
mu1  <- rep(0,k); del  <- 0.4; mu2 <- mu1 + rep(del, k);
sig1 <- diag(k); sig2 <- sig1 + del*toeplitz(c(1,rep(0.5, k-1)))
alt.dist.samples <- Sum_of_Wishart_df(total_sample_size=150,
sig1=sig1, sig2=sig2, alloc.ratio=c(2,1))