denpoly: Coefficients of the Denominator Polynomial for \tilde{H}_k...

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

Coefficients of the Denominator Polynomial for \tilde{H}_k and \tilde{C}_k

Description

This function computes the coefficients of the denominator polynomial for the elements of \tilde{H}_k and \tilde{C}_k. The function returns a vector containing the coefficients in descending powers of \tilde{n}, with the last element being the coefficient of \tilde{n}.

Usage

denpoly(k, alpha = 2)

Arguments

k	The order of the polynomial (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 vector containing the coefficients of the denominator polynomial in descending powers of \tilde{n} for the elements of \tilde{H}_k and \mathcal{C}_k.

Examples

# Example 1: Compute the denominator polynomial for k = 3, alpha = 2
# Output corresponds to the polynomial n1^5-3n1^4-8n1^3+12n1^2+16n1,
# where n1 is \eqn{\tilde{n}}
denpoly(3)

# Example 2: Compute the denominator polynomial for k = 2, alpha = 1
# Output corresponds to the polynomial n1^3-n1, where n1 is \eqn{\tilde{n}}
denpoly(2, alpha = 1)

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