qk_coeff: Coefficient Matrix \mathcal{C}_k

In wishmom: Compute Moments Related to Beta-Wishart and Inverse Beta-Wishart Distributions

Coefficient Matrix \mathcal{C}_k

Description

This function computes the coefficient matrix \mathcal{C}_k, which is a matrix of constants that allows us to obtain E[p_{\lambda}(W)W^r], where r+|\lambda|=k and W \sim W_m^{\beta}(n, \Sigma).

Usage

qk_coeff(k, alpha = 2)

Arguments

k	The order of the \mathcal{C}_k matrix
alpha	The type of Wishart distribution (\alpha=2/\beta): 1/2: Quaternion Wishart 1: Complex Wishart 2: Real Wishart (default)

Value

\mathcal{C}_k, a matrix that allows us to obtain E[p_{\lambda}(W)W^r], where r+|\lambda|=k and W \sim W_m^{\beta}(n, \Sigma). The matrix is represented as a 3-dimensional array where each slice along the third dimension represents a coefficient matrix of the polynomial in descending powers of n.

Examples

# Example 1:
qk_coeff(2) # For real Wishart distribution with k = 2

# Example 2:
qk_coeff(3, 1) # For complex Wishart distribution with k = 3

# Example 3:
qk_coeff(2, 1/2) # For quaternion Wishart distribution with k = 2

wishmom documentation built on Sept. 11, 2024, 8:29 p.m.