wishmom (version 1.1.0)

dkmap: Mapping Matrix that maps \(Q_{k+1}\) to \(Q_k\) for a beta-Wishart Distribution, but without \(n\) on the diagonal

Description

This function computes the matrix that maps \(Q_{k+1}\) to \(Q_k\) when \(W \sim W_m^{\beta}(n, \Sigma)\).

Usage

dkmap(k, alpha = 2)

Value

A matrix that maps \(Q_{k+1}\) to \(Q_k\), but without \(n\) on the diagonal.

Arguments

k

The order of the mapping matrix \(D_k\) (a positive integer)

alpha

The type of beta-Wishart distribution (\(\alpha=2/\beta\)):

• 1/2: Quaternion Wishart

• 1: Complex Wishart

• 2: Real Wishart (default)

Examples

# Example 1: Compute the mapping matrix for k = 2, real Wishart
dkmap(2)
# Example 2: Compute the mapping matrix for k = 1, complex Wishart
dkmap(1, 1)
# Example 3: Compute the mapping matrix for k = 2, quaternion Wishart
dkmap(2, 1/2)