qkn_coeffr: Coefficient Matrix \tilde{C}_k

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

Coefficient Matrix \tilde{C}_k

Description

This function computes the coefficient matrix for \tilde{\mathcal{C}}_k for W \sim W_m^{\beta}(n, \Sigma).

Usage

qkn_coeffr(k, alpha = 2)

Arguments

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

Value

A list with two elements:

• c: A 3-dimensional array containing the coefficient matrices of the numerator of \tilde{\mathcal{C}}_k in descending powers of n1, where n1 = n - m + 1 - \alpha.

• den: A vector containing the coefficients of the denominator of \tilde{\mathcal{C}}_k, in descending powers of n1.

Examples

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

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

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

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