iwish_ps: Inverse of a Coefficient Matrix \tilde{\mathcal{H}}_k

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

Inverse of a Coefficient Matrix \tilde{\mathcal{H}}_k

Description

This function computes the inverse of a coefficient matrix \tilde{\mathcal{H}}_k that allows us to compute the expected value of a power-sum symmetric function of W^{-1}, where W \sim W_m^{\beta}(n,\Sigma).

Usage

iwish_ps(k, alpha = 2)

Arguments

k	The order of the \tilde{\mathcal{H}}_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

Inverse of a coefficient matrix \tilde{\mathcal{H}}_k that allows us to compute the expected value of a power-sum symmetric function of W^{-1}, where 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 \tilde{n}.

Examples

# Example 1:
iwish_ps(3) # For real Wishart distribution with k = 3

# Example 2:
iwish_ps(4, 1) # For complex Wishart distribution with k = 4

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

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